base_11.txt

0, 1, 5, 13, 41, 53, 55, 60, 61, 90, 97, 169, 185, 193, 215, 265, 269, 353, 355, 385, 397, 437, 
481, 493, 617, 629, 630, 653, 713, 750, 769, 780, 889, 905, 960, 1013, 1025, 1045, 1205, 1320, 
1405, 1435, 1501, 1620, 1650, 1657, 1705, 1735, 1769, 1793, 1913, 1981, 2125, 2153, 2280, 2297, 
2389, 2413, 2460, 2465, 2509, 2533, 2549, 2609, 2610, 2633, 2730, 2749, 2845, 2893, 2915, 3041, 
3055, 3155, 3209, 3360, 3475, 3485, 3521, 3641, 3721, 3749, 3757, 3761, 3840, 3865, 3929, 3941, 
4075, 4273, 4301, 4650, 4937, 5195, 5209, 5435, 5489, 5490, 5700, 5917, 6169, 6253, 6335, 6361, 
6373, 6401, 6581, 6593, 6701, 6750, 6941, 7021, 7349, 7577, 7595, 7693, 7740, 7805, 7873, 8009, 
8017, 8215, 8341, 8495, 8737, 8861, 8970, 8995, 9120, 9133, 9181, 9269, 9277, 9535, 9541, 9737, 
9935, 9953, 10297, 10609, 10789, 10855, 11317, 11809, 12029, 12175, 12353, 12461, 12565, 12805, 
12893, 13855, 14381, 14550, 14935, 15055, 15115, 15289, 15637, 15709, 16177, 16789, 16837, 17065, 
17237, 17605, 17681, 17873, 17941, 17993, 18193, 18257, 18421, 18515, 18733, 18865, 18990, 19135, 
19140, 19375, 19453, 19657, 19873, 20035, 20400, 20405, 20797, 20881, 21133, 21293, 21305, 21865, 
22201, 22345, 22440, 22805, 23340, 23353, 24005, 24173, 24289, 24575, 24835, 24917, 25133, 25453, 
25457, 25741, 25775, 26333, 26453, 26681, 26915, 26933, 27005, 27013, 27240, 28277, 28555, 28717, 
29225, 29233, 29521, 29645, 29713, 29761, 29921, 30437, 30457, 31135, 31201, 31229, 31513, 32761, 
33180, 33529, 33557, 34475, 34609, 34625, 34830, 35070, 35100, 36013, 36377, 36577, 36749, 37201, 
37561, 37675, 37721, 37781, 37829, 38437, 38657, 38760, 38813, 39395, 39689, 40475, 40853, 41657, 
42445, 42509, 42889, 43073, 43170, 43950, 45161, 46013, 46369, 46885, 47197, 47513, 47921, 48810, 
48865, 49697, 49975, 50095, 50329, 50365, 51241, 51413, 51625, 51769, 51805, 53280, 53965, 54265, 
55373, 55649, 55697, 55921, 56395, 56605, 56693, 57360, 58493, 58729, 61500, 61961, 62155, 62281, 
62669, 63149, 63281, 63841, 64200, 66115, 67117, 67633, 68033, 68165, 68557, 69133, 69193, 70505, 
70529, 71201, 71335, 72593, 72797, 74005, 74485, 74705, 76073, 76181, 77033, 77573, 77790, 78077, 
78349, 79050, 79097, 79813, 81180, 82015, 82889, 83857, 84281, 84361, 84870, 86081, 88049, 88361, 
88837, 89009, 90581, 90925, 91093, 91381, 91973, 93317, 93360, 93655, 93701, 94433, 95453, 96025, 
96035, 96353, 96541, 96913, 98029, 99053, 99145, 99661, 100721, 101335, 101693, 102529, 102995, 
102997, 103565, 103813, 104417, 106837, 106913, 107137, 108060, 108097, 111277, 111865, 112025, 
113245, 114833, 115501, 116413, 116610, 116857, 117265, 117595, 117869, 118255, 118410, 118517, 
119701, 120055, 121081, 121561, 122693, 122857, 123589, 124535, 125309, 125861, 125885, 125975, 
126755, 128345, 129235, 129257, 130121, 131081, 131249, 131341, 131370, 133813, 135493, 136649, 
138421, 138713, 138961, 140155, 140341, 140417, 141113, 141120, 141473, 142045, 144265, 144529, 
145721, 147941, 148500, 149321, 152045, 152809, 153120, 153689, 154721, 154973, 156097, 156690, 
156780, 159097, 160093, 160697, 161249, 162481, 162510, 162935, 163777, 163889, 164041, 164315, 
164873, 165049, 168229, 169333, 170880, 171089, 172409, 173809, 173940, 174870, 178775, 179813, 
180780, 183913, 184169, 185537, 185737, 185975, 186269, 187475, 189275, 189845, 190165, 191225, 
191790, 191917, 194695, 195540, 195613, 196013, 198877, 199153, 201701, 201721, 203105, 203575, 
203795, 204781, 206473, 209713, 211950, 215597, 218933, 218981, 219677, 220170, 221201, 221569, 
222510, 223477, 224921, 226355, 228661, 231505, 231793, 231797, 233250, 233305, 233677, 234433, 
238237, 238333, 239489, 239569, 241489, 243120, 243840, 243960, 244140, 245465, 246275, 246570, 
247409, 252750, 254135, 255329, 258065, 258493, 258655, 259055, 261997, 266375, 266413, 266580, 
268145, 269915, 269941, 270089, 274517, 275797, 276605, 276840, 277837, 277853, 278285, 280805, 
281465, 282180, 282937, 283165, 284261, 285269, 287555, 293401, 294305, 294475, 297733, 299765, 

fib_n.c

#include <malloc.h>
#include <stdio.h>
#include <gmp.h>



int main()
{
    int B = 11;
    char digits[256];

    mpz_t a;
    mpz_t b;
    mpz_t c;

    int a_0;
    int b_0;
    int c_0;

    for (int c = 0; c < 256; c++) {
        digits[c] = -1;
    }
    for (int c = '0'; c <= '9'; c++) {
        digits[c] = c - '0';
    }

    if (B > 36) {
        for (int c = 'a'; c <= 'z'; c++) {
            digits[c] = c + 36 - 'a';
        }
        for (int c = 'A'; c <= 'Z'; c++) {
            digits[c] = c + 10 - 'A';
        }
    } else {
        for (int c = 'a'; c <= 'z'; c++) {
            digits[c] = c + 10 - 'a';
        }
    }

    mpz_init(a);
    mpz_init(b);
    mpz_init(c);
    mpz_set_ui(a, 0);
    mpz_set_ui(b, 1);


    a_0 = 0;
    b_0 = 1;
    for (int i = 0;; i++) {
        if (a_0 == i % (B - 1)) {
            char *str;
            str = mpz_get_str(NULL, B, a);

            int sum = 0;
            for (int j = 0; str[j]; j++) {
                sum += digits[str[j]];
            }

            if (sum == i) {
                gmp_fprintf(stdout, "\n%d: %Zd\n\n", i, a);
            } else {
                fprintf(stdout, "%c", sum > i ? '>' : '<');
            }
            free(str);
        }
        mpz_add(c, a, b);
        mpz_swap(a, b);
        mpz_swap(b, c);

        c_0 = (a_0 + b_0) % (B - 1);
        a_0 = b_0;
        b_0 = c_0;

    }

    mpz_clear(c);
    mpz_clear(b);
    mpz_clear(a);
    return 0;
}

fib_n.hs

fibs = 0:1:zipWith (+) fibs (tail fibs)

digitsOf b x = reverse $ map (`mod` b) $ takeWhile (/= 0) $ iterate (`div` b) x

main = mapM_ print $ take 1000 [(b,[n | (n,a) <- take 3000 $ zip [0..] fibs, (sum $ digitsOf b a) == n]) | b <- [2..]]

log

(2,[0,1])
(3,[0,1])
(4,[0,1])
(5,[0,1])
(6,[0,1,5,9,15,35])
(7,[0,1,5,7,11,12,53])
(8,[0,1,5,22,41])
(9,[0,1,5,29,77,149,312])
(10,[0,1,5,10,31,35,62,72,175,180,216,251,252,360,494,504,540,946,1188,2222])
(11,[0,1,5,13,41,53,55,60,61,90,97,169,185,193,215,265,269,353,355,385,397,437,481,493,617,629,630,653,713,750,769,780,889,905,960,1013,1025,1045,1205,1320,1405,1435,1501,1620,1650,1657,1705,1735,1769,1793,1913,1981,2125,2153,2280,2297,2389,2413,2460,2465,2509,2533,2549,2609,2610,2633,2730,2749,2845,2893,2915])
(12,[0,1,5,13,14,89,96,123,221,387,419,550,648,749,866,892,1105,2037])
(13,[0,1,5,12,24,25,36,48,53,72,73,132,156,173,197,437,444,485,696,769,773])
(14,[0,1,5,8,11,27,34,181,192,194])
(15,[0,1,5])
(16,[0,1,5,10,60,101])
(17,[0,1,5])
(18,[0,1,5,60])
(19,[0,1,5,31,36])
(20,[0,1,5,21,22])
(21,[0,1,5,13,17,25,29,61])
(22,[0,1,5,60])
(23,[0,1,5,12,13])
(24,[0,1,5,21])
(25,[0,1,5,25])
(26,[0,1,5,9,21,29])
(27,[0,1,5,11])
(28,[0,1,5])
(29,[0,1,5,41])
(30,[0,1,5])
(31,[0,1,5,25,29,55])
(32,[0,1,5,32,34])
(33,[0,1,5])
(34,[0,1,5,12,14])
(35,[0,1,5])
(36,[0,1,5])
(37,[0,1,5])
(38,[0,1,5,35])
(39,[0,1,5,30])
(40,[0,1,5,11,34])
(41,[0,1,5])
(42,[0,1,5,43])
(43,[0,1,5])
(44,[0,1,5])
(45,[0,1,5,12,13])
(46,[0,1,5,10])
(47,[0,1,5])
(48,[0,1,5])
(49,[0,1,5])
(50,[0,1,5,22])
(51,[0,1,5])
(52,[0,1,5])
(53,[0,1,5])
(54,[0,1,5])
(55,[0,1,5])
(56,[0,1,5,13])
(57,[0,1,5])
(58,[0,1,5])
(59,[0,1,5,30])
(60,[0,1,5])
(61,[0,1,5])
(62,[0,1,5])
(63,[0,1,5])
(64,[0,1,5])
(65,[0,1,5])
(66,[0,1,5])
(67,[0,1,5,12])
(68,[0,1,5])
(69,[0,1,5])
(70,[0,1,5])
(71,[0,1,5])
(72,[0,1,5])
(73,[0,1,5])
(74,[0,1,5])
(75,[0,1,5])
(76,[0,1,5,29,49])
(77,[0,1,5])
(78,[0,1,5])
(79,[0,1,5,11])
(80,[0,1,5])
(81,[0,1,5])
(82,[0,1,5])
(83,[0,1,5])
(84,[0,1,5])
(85,[0,1,5])
(86,[0,1,5,15])
(87,[0,1,5])
(88,[0,1,5])
(89,[0,1,5])
(90,[0,1,5])
(91,[0,1,5])
(92,[0,1,5])
(93,[0,1,5])
(94,[0,1,5])
(95,[0,1,5])
(96,[0,1,5,21])
(97,[0,1,5])
(98,[0,1,5])
(99,[0,1,5])
(100,[0,1,5])
(101,[0,1,5])
(102,[0,1,5])
(103,[0,1,5])
(104,[0,1,5])
(105,[0,1,5])
(106,[0,1,5])
(107,[0,1,5])
(108,[0,1,5])
(109,[0,1,5])
(110,[0,1,5])
(111,[0,1,5,13])
(112,[0,1,5])
(113,[0,1,5])
(114,[0,1,5])
(115,[0,1,5])
(116,[0,1,5])
(117,[0,1,5])
(118,[0,1,5])
(119,[0,1,5])
(120,[0,1,5,15])
(121,[0,1,5,25])
(122,[0,1,5,14])
(123,[0,1,5])
(124,[0,1,5])
(125,[0,1,5])
(126,[0,1,5])
(127,[0,1,5])
(128,[0,1,5])
(129,[0,1,5])
(130,[0,1,5])
(131,[0,1,5])
(132,[0,1,5])
(133,[0,1,5,12])
(134,[0,1,5])
(135,[0,1,5])
(136,[0,1,5])
(137,[0,1,5])
(138,[0,1,5])
(139,[0,1,5])
(140,[0,1,5])
(141,[0,1,5])
(142,[0,1,5])
(143,[0,1,5])
(144,[0,1,5])
(145,[0,1,5])
(146,[0,1,5])
(147,[0,1,5])
(148,[0,1,5])
(149,[0,1,5])
(150,[0,1,5])
(151,[0,1,5])
(152,[0,1,5])
(153,[0,1,5])
(154,[0,1,5])
(155,[0,1,5])
(156,[0,1,5])
(157,[0,1,5])
(158,[0,1,5])
(159,[0,1,5,17])
(160,[0,1,5])
(161,[0,1,5])
(162,[0,1,5])
(163,[0,1,5])
(164,[0,1,5,35])
(165,[0,1,5])
(166,[0,1,5])
(167,[0,1,5])
(168,[0,1,5])
(169,[0,1,5])
(170,[0,1,5])
(171,[0,1,5])
(172,[0,1,5])
(173,[0,1,5])
(174,[0,1,5])
(175,[0,1,5])
(176,[0,1,5])
(177,[0,1,5])
(178,[0,1,5])
(179,[0,1,5])
(180,[0,1,5])
(181,[0,1,5])
(182,[0,1,5])
(183,[0,1,5])
(184,[0,1,5])
(185,[0,1,5])
(186,[0,1,5])
(187,[0,1,5])
(188,[0,1,5])
(189,[0,1,5])
(190,[0,1,5])
(191,[0,1,5])
(192,[0,1,5])
(193,[0,1,5])
(194,[0,1,5])
(195,[0,1,5])
(196,[0,1,5])
(197,[0,1,5])
(198,[0,1,5,49])
(199,[0,1,5])
(200,[0,1,5])
(201,[0,1,5])
(202,[0,1,5])
(203,[0,1,5])
(204,[0,1,5])
(205,[0,1,5])
(206,[0,1,5])
(207,[0,1,5])
(208,[0,1,5])
(209,[0,1,5])
(210,[0,1,5])
(211,[0,1,5])
(212,[0,1,5])
(213,[0,1,5])
(214,[0,1,5])
(215,[0,1,5])
(216,[0,1,5])
(217,[0,1,5])
(218,[0,1,5])
(219,[0,1,5])
(220,[0,1,5])
(221,[0,1,5,13])
(222,[0,1,5])
(223,[0,1,5])
(224,[0,1,5])
(225,[0,1,5])
(226,[0,1,5])
(227,[0,1,5])
(228,[0,1,5])
(229,[0,1,5])
(230,[0,1,5])
(231,[0,1,5])
(232,[0,1,5])
(233,[0,1,5])
(234,[0,1,5])
(235,[0,1,5])
(236,[0,1,5])
(237,[0,1,5])
(238,[0,1,5])
(239,[0,1,5])
(240,[0,1,5])
(241,[0,1,5])
(242,[0,1,5])
(243,[0,1,5])
(244,[0,1,5])
(245,[0,1,5])
(246,[0,1,5])
(247,[0,1,5])
(248,[0,1,5])
(249,[0,1,5])
(250,[0,1,5])
(251,[0,1,5])
(252,[0,1,5])
(253,[0,1,5])
(254,[0,1,5])
(255,[0,1,5])
(256,[0,1,5])
(257,[0,1,5])
(258,[0,1,5])
(259,[0,1,5])
(260,[0,1,5])
(261,[0,1,5])
(262,[0,1,5])
(263,[0,1,5])
(264,[0,1,5])
(265,[0,1,5])
(266,[0,1,5])
(267,[0,1,5])
(268,[0,1,5])
(269,[0,1,5])
(270,[0,1,5])
(271,[0,1,5])
(272,[0,1,5])
(273,[0,1,5])
(274,[0,1,5])
(275,[0,1,5])
(276,[0,1,5])
(277,[0,1,5])
(278,[0,1,5])
(279,[0,1,5])
(280,[0,1,5])
(281,[0,1,5])
(282,[0,1,5])
(283,[0,1,5])
(284,[0,1,5])
(285,[0,1,5])
(286,[0,1,5])
(287,[0,1,5])
(288,[0,1,5])
(289,[0,1,5])
(290,[0,1,5])
(291,[0,1,5])
(292,[0,1,5])
(293,[0,1,5])
(294,[0,1,5])
(295,[0,1,5])
(296,[0,1,5])
(297,[0,1,5])
(298,[0,1,5])
(299,[0,1,5])
(300,[0,1,5])
(301,[0,1,5])
(302,[0,1,5])
(303,[0,1,5,30])
(304,[0,1,5])
(305,[0,1,5])
(306,[0,1,5])
(307,[0,1,5])
(308,[0,1,5])
(309,[0,1,5])
(310,[0,1,5])
(311,[0,1,5])
(312,[0,1,5])
(313,[0,1,5])
(314,[0,1,5])
(315,[0,1,5])
(316,[0,1,5])
(317,[0,1,5,17])
(318,[0,1,5])
(319,[0,1,5])
(320,[0,1,5])
(321,[0,1,5])
(322,[0,1,5])
(323,[0,1,5])
(324,[0,1,5])
(325,[0,1,5])
(326,[0,1,5])
(327,[0,1,5])
(328,[0,1,5])
(329,[0,1,5])
(330,[0,1,5])
(331,[0,1,5])
(332,[0,1,5])
(333,[0,1,5])
(334,[0,1,5])
(335,[0,1,5])
(336,[0,1,5])
(337,[0,1,5])
(338,[0,1,5])
(339,[0,1,5])
(340,[0,1,5])
(341,[0,1,5])
(342,[0,1,5])
(343,[0,1,5])
(344,[0,1,5])
(345,[0,1,5])
(346,[0,1,5])
(347,[0,1,5])
(348,[0,1,5])
(349,[0,1,5])
(350,[0,1,5])
(351,[0,1,5])
(352,[0,1,5])
(353,[0,1,5])
(354,[0,1,5])
(355,[0,1,5])
(356,[0,1,5,20])
(357,[0,1,5])
(358,[0,1,5])
(359,[0,1,5])
(360,[0,1,5])
(361,[0,1,5])
(362,[0,1,5])
(363,[0,1,5])
(364,[0,1,5,14])
(365,[0,1,5])
(366,[0,1,5])
(367,[0,1,5])
(368,[0,1,5])
(369,[0,1,5])
(370,[0,1,5])
(371,[0,1,5])
(372,[0,1,5])
(373,[0,1,5])
(374,[0,1,5])
(375,[0,1,5])
(376,[0,1,5])
(377,[0,1,5])
(378,[0,1,5])
(379,[0,1,5])
(380,[0,1,5])
(381,[0,1,5])
(382,[0,1,5])
(383,[0,1,5])
(384,[0,1,5])
(385,[0,1,5])
(386,[0,1,5])
(387,[0,1,5])
(388,[0,1,5])
(389,[0,1,5])
(390,[0,1,5])
(391,[0,1,5])
(392,[0,1,5])
(393,[0,1,5])
(394,[0,1,5])
(395,[0,1,5])
(396,[0,1,5,17])
(397,[0,1,5])
(398,[0,1,5])
(399,[0,1,5])
(400,[0,1,5])
(401,[0,1,5])
(402,[0,1,5])
(403,[0,1,5])
(404,[0,1,5])
(405,[0,1,5])
(406,[0,1,5])
(407,[0,1,5])
(408,[0,1,5])
(409,[0,1,5])
(410,[0,1,5])
(411,[0,1,5])
(412,[0,1,5])
(413,[0,1,5])
(414,[0,1,5])
(415,[0,1,5])
(416,[0,1,5])
(417,[0,1,5])
(418,[0,1,5])
(419,[0,1,5])
(420,[0,1,5])
(421,[0,1,5])
(422,[0,1,5])
(423,[0,1,5])
(424,[0,1,5])
(425,[0,1,5])
(426,[0,1,5])
(427,[0,1,5])
(428,[0,1,5])
(429,[0,1,5])
(430,[0,1,5])
(431,[0,1,5])
(432,[0,1,5])
(433,[0,1,5])
(434,[0,1,5])
(435,[0,1,5])
(436,[0,1,5])
(437,[0,1,5])
(438,[0,1,5])
(439,[0,1,5])
(440,[0,1,5])
(441,[0,1,5])
(442,[0,1,5])
(443,[0,1,5])
(444,[0,1,5])
(445,[0,1,5])
(446,[0,1,5])
(447,[0,1,5])
(448,[0,1,5])
(449,[0,1,5])
(450,[0,1,5])
(451,[0,1,5])
(452,[0,1,5])
(453,[0,1,5])
(454,[0,1,5])
(455,[0,1,5])
(456,[0,1,5])
(457,[0,1,5])
(458,[0,1,5])
(459,[0,1,5])
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