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%I #16 Jul 23 2023 01:54:10
%S 1,64,127,1057,1090,1156,1288,1519,1552,1783,1915,1981,2014,4369,4642,
%T 5188,6007,6280,7099,7645,7918,16963,17029,17161,17542,17545,17674,
%U 17938,18529,18577,18700,18706,18964,19492,20335,20641,20674,20770,21016,21028,21544,22447,22600,23479,23503,23995,24187,24253,24286,24865,24898,24964
%N Those terms of A255571 whose every A080541/A080542-rotation is also a term of A255571.
%C These are the numbers whose binary representation traces a nonselfcrossing circuit in honeycomb lattice when its bits (from the least to the second most significant bit; the most significant 1-bit is ignored) are interpreted as directions to proceed at each vertex, with an additional condition that the final direction (angle) must be equal to the starting direction of the walk. Because each bit either adds or subtracts 60 degrees from the current phase angle, it implies that for all terms after the initial term a(1)=0 (which stands for an empty path), the difference between the number of 0-bits and 1-bits (when excluding the most significant bit which is always 1) must be either -6 or +6. And indeed, for all n >= 1, A037861(a(n)) is either 5 or -7 as A037861 takes also the most significant bit into account.
%H Antti Karttunen, <a href="/A258001/b258001.txt">Table of n, a(n) for n = 0..13242</a> (all terms up to binary width 24+1)
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A258001 (MATCHING-POS 0 1 (lambda (n) (and (isA255571? n) (isA255571? (A080542 n)))))) ;; See also the code in A255571 and A080542.
%Y Subsequence of A255571.
%Y Cf. A037861, A080541, A080542.
%Y Cf. A258002 (a subsequence; terms that have more ones than zeros in their binary representation).
%K nonn,base
%O 0,2
%A _Antti Karttunen_, May 16 2015