cp's OEIS Frontend

A110562 Numbers n such that n in binary representation has a block of exactly a nontrivial pentagonal number of zeros.

%I A110562 #16 Sep 11 2024 14:15:04
%S A110562 32,65,96,130,131,160,193,224,260,261,262,263,288,321,352,386,387,416,
%T A110562 449,480,520,521,522,523,524,525,526,527,544,577,608,642,643,672,705,
%U A110562 736,772,773,774,775,800,833,864,898,899,928,961,992,1040,1041,1042
%N A110562 Numbers n such that n in binary representation has a block of exactly a nontrivial pentagonal number of zeros.
%C A110562 a(n) is the index of zeros in the complement of the pentagonal number analog of the Baum-Sweet sequence, which is b(n) = 1 if the binary representation of n contains no block of consecutive zeros of exactly a nontrivial pentagonal number length A000326(i) for i>1; otherwise b(n) = 0.
%D A110562 J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 157.
%H A110562 J.-P. Allouche, <a href="http://www.mat.univie.ac.at/~slc/s/s30allouche.html">Finite Automata and Arithmetic</a>, Séminaire Lotharingien de Combinatoire, B30c (1993), 23 pp.
%e A110562 a(1) = 32 because 32 (base 2) = 100000, which has a block of 5 = A000326(2) zeros.
%e A110562 a(2) = 65 because 65 (base 2) = 1000001, which has a block of 5 zeros.
%e A110562 64 is not in this sequence because, though 64 (base 2) = 1000000 has a block of 6 zeros, which has subblocks of 5 zeros, subblocks do not count.
%e A110562 2080 is in this sequence because 2080 (base 2) = 100000100000 has 2 blocks of 5 zeros, but we do not require only one such 5-zero block.
%e A110562 4096 is in this sequence because 4096 (base 2) = 1000000000000, which has a block of 12 = A000326(3) zeros, as do 8193 and many more.
%e A110562 4194304 is in this sequence because 4194304 (base 2) = 10000000000000000000000, which has a block of 22 = A000326(4) zeros.
%Y A110562 Cf. A000326, A037011, A086747, A110471, A110472, A110474, A110502, A110529.
%K A110562 base,easy,nonn
%O A110562 1,1
%A A110562 _Jonathan Vos Post_, Sep 12 2005
%E A110562 Corrected by _Ray Chandler_, Sep 17 2005