Example Adar programs that generate OEIS sequences

Adar.py

# Adar implementation from
# https://esolangs.org/wiki/Adar

adar = lambda l: (lambda n: list(map(lambda x: (x[0] + n, x[1]), l)))(sum(map(lambda x: (x[0] >= 0) * x[1], l)))

# Basic code that I wrote to run & trace Adar programs

# prints only the value of the first register at each step
def run(prog, steps=10, outputInitial = False, adar=adar):
    output = []
    if outputInitial:
        output.append(prog[0][0])
        print prog[0][0],
    for n in range(steps):
        prog = adar(prog)
        output.append(prog[0][0])
        print prog[0][0],
    print
    return output

# prints the state of prog at each step
def trace(prog, steps=10, adar=adar):
    print prog
    for n in range(steps):
        prog = adar(prog)
        print prog
    print

# Creates an Adar program whose first register takes on the values in seq.
# If initialState is not given, then the first value in seq is used.
# DOES NOT WORK FOR ALL SEQUENCES!
def SequenceToAdarProgram(seq, initialState = None):
    prog = []
    idx = 0
    if initialState == None:
        initialState = seq[0]
        idx = 1
    # make the first register
    prog.append((initialState, seq[0] - initialState))
    lastval = seq[0] 
    # make additional registers
    for val in seq[idx:]:
        lastdiff = val - lastval
        initialdiff = lastval - initialState
        # sum the offsets of all registers that will trigger during this step
        totaloffset = 0
        for reg in prog:
            if reg[0] + initialdiff >= 0:
                totaloffset += reg[1]
        # new register should trigger on lastval and add an offset to reach val
        newoffset = val - (lastval + totaloffset)
        prog.append((-initialdiff, newoffset))
        lastval = val
    # add a final register to halt the program
    prog.append((initialState-lastval, -(lastval+1)))

    return prog

Adar_programs.py

# Example Adar programs

from Adar import *

ex = [(0,2),(-2,5),(-3,-2),(-6,-7),(-8,1)]

# powers of 2
pow2max = 1024
pow2 = [(-i,1) for i in range(pow2max+1)]
pow2[0] = (1,1)
pow2[pow2max] = (-pow2max,-2*(pow2max+1))

# powers of 3
pow3max = 59049
pow3 = [(-i,2) for i in range(pow3max+1)]
pow3[0] = (1,2)
pow3[pow3max] = (-pow3max,-3*(pow3max+1)) 

def powersOfN(n, maxexp=10):
    maxval = n**maxexp
    powers = [(-i,n-1) for i in range(maxval+1)]
    powers[0] = (1,n-1)
    powers[maxval] = (-maxval,-n*(maxval+1))
    return powers

# divide by 3 on each step
# note that extra registers will throw off the results
div3 =  [(99,0)]
div3 += [(3*n+1,-1) for n in range(33)]
div3 += [(3*n+2,-1) for n in range(33)]

div3a =  [(214,0)]
div3a += [(3*n+1,-1) for n in range(72)]
div3a += [(3*n+2,-1) for n in range(71)]

# n! for n=1 to 7
fact = [(0,1), (-1,-1), (-1,1), (-2,3), (-6,14), (-24,78), (-120,504), (-720,3720)]

# This calculates the first 7 numbers in sequence A006893
# https://oeis.org/A006893
# a[0] = 1, a[n+1] = a[n] + tri(a[n]) where tri(i) is the ith triangular number
trisum = [(0,1)] + [(-n,n) for n in range(2,26800)]

# This calculates the first 11 numbers in sequence A006999 (increase 101 for more) 
# https://oeis.org/A006999
alt = [(-n,1) for n in range(0,101,2)]

# This calculates the first 22 numbers in sequence A155167,
# which is defined as "(L)-sieve transform of {3,7,11,15,...,4n-1,...}"
# and appears to be equal to a(n)=Floor[(4*a[[n-1]]+3)/3].
# https://oeis.org/A155167
every3rd = [(-n,1) for n in range(0,1000,3)]

# This calculates the first 38 numbers in sequence A279075,
# which is defined as "Maximum starting value of X such that repeated replacement
# of X with X-ceiling(X/5) requires n steps to reach 0." and has the formula
# a(n) = floor(a(n-1)*5/4) + 1. Conjectured to be the (L)-sieve transform of
# {4,9,14,19,...,5n-1,...}".
# https://oeis.org/A279075
every4th = [(-n,1) for n in range(0,10400,4)]

# Similarly,
allones  = [(-n,1) for n in range(0,10000,1)]   # https://oeis.org/A000225 = 2^n - 1
every5th = [(-n,1) for n in range(0,10000,5)]   # https://oeis.org/A279076
every6th = [(-n,1) for n in range(0,10000,6)]   # https://oeis.org/A279077
every7th = [(-n,1) for n in range(0,10000,7)]   # https://oeis.org/A279078
every8th = [(-n,1) for n in range(0,10000,8)]   # https://oeis.org/A279079
every9th = [(-n,1) for n in range(0,10000,9)]   # https://oeis.org/A279080