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A352336 Define a sequence B = {b(i): i >= 1} by b(i) = smallest unused number when A109812(i) is being calculated, and then remove duplicates from B.

%I A352336 #28 May 03 2024 15:03:26
%S A352336 1,2,3,5,6,7,11,13,15,22,23,27,28,29,30,31,43,46,47,55,61,63,87,91,93,
%T A352336 94,95,123,125,126,127,189,191,222,223,235,237,238,239,247,251,254,
%U A352336 255,319,373,375,379,381,383,431,439,443,446,447,475,479,495,499,503,506,507,509,511,765,767,895,959,989,991,1007,1023,1503,1519,1531,1535,1783
%N A352336 Define a sequence B = {b(i): i >= 1} by b(i) = smallest unused number when A109812(i) is being calculated, and then remove duplicates from B.
%C A352336 Might be called the local minima in A109812.
%C A352336 Also indices of records in A113233. These are the numbers that are the slowest to appear in A109812. They arrive late in A109812 because of having few zeros in their binary expansion. Every number of the form 2^k - 1 is necessarily a member, since any number less than 2^k - 1 must occur earlier in A109812. - _David Broadhurst_, Aug 17 2022
%H A352336 N. J. A. Sloane, <a href="/A352336/b352336.txt">Table of n, a(n) for n = 1..221</a>
%H A352336 David Broadhurst, <a href="/A352359/a352359.txt">Table of n, A352336(n), A352359(n) for n = 1..221</a>
%e A352336 The initial terms of A109812 and the smallest missing numbers (smn):
%e A352336   n a(n) smn
%e A352336   1  1   2
%e A352336   2  2   3
%e A352336   3  4   3
%e A352336   4  3   5
%e A352336   5  8   5
%e A352336   6  5   6
%e A352336   7  10  6
%e A352336   8  16  6
%e A352336   9   6  7
%e A352336   10  9  7
%e A352336   11  18 7
%e A352336   12  12 7
%e A352336   ...
%e A352336 so the distinct smallest missing numbers are 1, 2, 3, 5, 6, 7, ...
%t A352336 c[_] = 0; a[1] = c[1] = 1; u = 2; {1}~Join~Reap[Do[k = u; While[Nand[c[k] == 0, BitAnd[a[i - 1], k] == 0], k++]; If[a[i - 1] == u, Sow[u]; While[c[u] > 0, u++]]; Set[{a[i], c[k]}, {k, i}], {i, 2, nn}]][[-1, -1]]
%Y A352336 Cf. A109812, A113233, A352203, A352359.
%K A352336 nonn,base
%O A352336 1,2
%A A352336 _Michael De Vlieger_, Mar 29 2022
%E A352336 Edited by _N. J. A. Sloane_, Apr 26 2022 and May 03 2024