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%I #14 Dec 20 2021 02:37:30
%S 0,1,2,3,4,6,7,8,12,14,15,16,24,26,28,30,31,32,48,52,56,58,60,62,63,
%T 64,96,100,104,106,112,118,120,122,124,126,127,128,192,200,208,212,
%U 224,228,234,236,240,246,248,250,252,254,255,256,384,392,400,416,420,424,426,448,460,466,472,474,480,484,490,494,496,502,504,506,508,510,511,512
%N Numbers k for which A256999(A059893(k)) = k.
%C Indexing starts from zero, because a(0) = 0 is a special case.
%C These numbers correspond to the maximal (lexicographically largest) representatives selected from each equivalence class of those binary necklaces that stay the same (in the same equivalence class) when flipped over (which thus have a bilateral symmetry, please see the examples). A029744(n) gives the number of terms with n significant bits in their binary representation.
%H Antti Karttunen, <a href="/A258209/b258209.txt">Table of n, a(n) for n = 0..5117</a>
%e 28 ("11100" in binary) is in sequence, because after removing the most significant bit, the binary string "1100" when reversed, "0011", can then be rotated (two steps in either direction) to give "1100" again and "1100" is the lexicographically largest of these rotations.
%e 114 ("1110010" in binary) is NOT in the sequence, because after removing the most significant bit, the binary string "110010" when reversed, "010011", does not yield "110010" no matter how many steps it is rotated (even though it is the lexicographically largest rotation of its class). Thus although 114 is in A257250 (a supersequence of this sequence), it is not included here.
%o (define (isA258209? n) (= n (A256999 (A059893 n))))
%o (define A258209 (MATCHING-POS 0 0 isA258209?))
%Y Cf. A029744, A059893, A256999.
%Y Subsequence of A257250.
%Y Differs from A257250 for the first time at n=31, where a(31) = 118, while A257250(31) = 114.
%K nonn,base
%O 0,3
%A _Antti Karttunen_, May 31 2015
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