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A258001 Those terms of A255571 whose every A080541/A080542-rotation is also a term of A255571. 2
1, 64, 127, 1057, 1090, 1156, 1288, 1519, 1552, 1783, 1915, 1981, 2014, 4369, 4642, 5188, 6007, 6280, 7099, 7645, 7918, 16963, 17029, 17161, 17542, 17545, 17674, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..13242; all terms up to the binary width 24+1

PROG

(Scheme, with Antti Karttunen's IntSeq-library)

(define A258001 (MATCHING-POS 0 1 (lambda (n) (and (isA255571? n) (isA255571? (A080542 n)))))) ;; See also the code in A255571 and A080542.

CROSSREFS

Subsequence of A255571.

Cf. A037861, A080541, A080542.

Cf. A258002 (a subsequence; terms that have more ones than zeros in their binary representation).

Sequence in context: A145464 A215558 A324487 * A255996 A296166 A044187

Adjacent sequences:  A257998 A257999 A258000 * A258002 A258003 A258004

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, May 16 2015

STATUS

approved

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Last modified July 28 11:14 EDT 2021. Contains 346326 sequences. (Running on oeis4.)