Generate keith numbers - OEIS A007629

keithnum.py

def iskeith(n):
    """Return True if n is a Keith number - https://oeis.org/A007629"""

    if n < 10:
        return False          # by definition

    # initial sequence seeding is the digits of n
    kl = [int(d) for d in str(n)]      # crude, but easy. Speed not relevant.
    ksum = sum(kl)

    while ksum < n:
        kl.append(ksum)
        ksum += ksum - kl.pop(0)
    return ksum == n


def keithnumbers(start=10, stop=10000):
    return (k for k in range(start, stop+1) if iskeith(k))


if __name__ == "__main__":
    import unittest

    class TestMethods(unittest.TestCase):
        # test values copy/pasted from Online Encyclopedia of
        # Integer Sequences https://oeis.org/A007629, but last
        # few numbers truncated because the algorithm takes a looong
        # time to reach them
        OEIS_SEQ_PARTIAL = [
            14, 19, 28, 47, 61, 75, 197, 742, 1104, 1537, 2208, 2580,
            3684, 4788, 7385, 7647, 7909, 31331, 34285, 34348, 55604,
            62662, 86935, 93993, 120284, 129106, 147640, 156146, 174680,
            183186, 298320, 355419, 694280, 925993, 1084051]
        OEIS_SEQ_SLOW = [7913837, 11436171, 33445755, 44121607]

        def test_keiths(self):
            for k in range(1, self.OEIS_SEQ_PARTIAL[-1] + 1):
                self.assertEqual(iskeith(k), k in self.OEIS_SEQ_PARTIAL)

        def test_generator(self):
            ks = list(self.OEIS_SEQ_PARTIAL)
            kmax = ks[-1]
            for k in keithnumbers(stop=kmax):
                self.assertEqual(k, ks.pop(0))

    unittest.main()