Template:Python calculate A190939

Python program to calculate the integer sequence

This code uses the Python library discrete helpers. from discretehelpers.a import make_linear_binv arity = 4 depth_to_seals = {depth: None for depth in range(arity)} depth_to_seals[0] = [make_linear_binv(walsh=0, parity=1, arity=arity)] # tautology depth_to_seals[1] = [make_linear_binv(walsh=i, parity=1, arity=arity) for i in range(1, 2 ** arity)] # negated Walsh functions for new_depth in range(2, arity+1): new_weight = 2 ** (arity - new_depth) old_depth = new_depth - 1 old_seals = depth_to_seals[old_depth] new_seals = set() for key_a, seal_a in enumerate(old_seals): for key_b in range(key_a + 1, len(old_seals)): seal_b = old_seals[key_b] candidate = seal_a & seal_b if candidate.weight == new_weight: new_seals.add(candidate) depth_to_seals[new_depth] = sorted(new_seals) lengths = [] sequence = [] for depth, seals in depth_to_seals.items(): rank = arity - depth seal_integers = sorted([seal.intval for seal in seals]) print(f'{rank}: {seal_integers},') lengths.append(len(seal_integers)) sequence += seal_integers print('\n', lengths) print('\n', sorted(sequence)) resulting dictionary rank_to_seals = { 4: [65535], 3: [255, 3855, 13107, 15555, 21845, 23205, 26265, 26985, 38505, 39321, 42405, 43605, 50115, 52275, 61455], 2: [15, 51, 85, 105, 153, 165, 195, 771, 1285, 1545, 2313, 2565, 3075, 4369, 4641, 5185, 6273, 8481, 8721, 9345, 10305, 12291, 16705, 17025, 17425, 18465, 20485, 24585, 33153, 33345, 33825, 34833, 36873, 40965, 49155], 1: [3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769], 0: [1] }