A352336 - OEIS

%I #28 May 03 2024 15:03:26

%S 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 94,95,123,125,126,127,189,191,222,223,235,237,238,239,247,251,254,

%U 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 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 Might be called the local minima in A109812.

%C 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 N. J. A. Sloane, <a href="/A352336/b352336.txt">Table of n, a(n) for n = 1..221</a>

%H David Broadhurst, <a href="/A352359/a352359.txt">Table of n, A352336(n), A352359(n) for n = 1..221</a>

%e The initial terms of A109812 and the smallest missing numbers (smn):

%e   n a(n) smn

%e   1  1   2

%e   2  2   3

%e   3  4   3

%e   4  3   5

%e   5  8   5

%e   6  5   6

%e   7  10  6

%e   8  16  6

%e   9   6  7

%e   10  9  7

%e   11  18 7

%e   12  12 7

%e   ...

%e so the distinct smallest missing numbers are 1, 2, 3, 5, 6, 7, ...

%t 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 Cf. A109812, A113233, A352203, A352359.

%K nonn,base

%O 1,2

%A _Michael De Vlieger_, Mar 29 2022

%E Edited by _N. J. A. Sloane_, Apr 26 2022 and May 03 2024