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Records in A175046.
4

%I #14 Nov 12 2018 12:43:08

%S 3,12,24,51,99,204,396,408,819,1587,1635,3276,6348,6540,6552,13107,

%T 25395,26163,26211,52428,101580,104652,104844,104856,209715,406323,

%U 418611,419379,419427,838860,1625292,1674444,1677516,1677708,1677720,3355443,6501171

%N Records in A175046.

%C a(n) in binary is either an alternating string of 11's and 00's, or exactly one of the 00's is replaced by 000 (see A319423). - _Chai Wah Wu_, Oct 04 2018

%H Chai Wah Wu, <a href="/A319422/b319422.txt">Table of n, a(n) for n = 1..10099</a>

%H Chai Wah Wu, <a href="https://arxiv.org/abs/1810.02293">Record values in appending and prepending bitstrings to runs of binary digits</a>, arXiv:1810.02293 [math.NT], 2018

%t b[n_] := (Append[#, #[[1]]]& /@ Split[IntegerDigits[n, 2]]) // Flatten // FromDigits[#, 2]&;

%t Reap[For[rec = 0; k = 1, k < 3000, k++, bk = b[k]; If[bk > rec, rec = bk; Sow[rec]]]][[2, 1]] (* _Jean-François Alcover_, Nov 12 2018 *)

%Y Cf. A175046, A319423, A319424 (written in binary).

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Sep 23 2018