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.

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

Offset

1,2

Comments

Might be called the local minima in A109812.

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

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..221

David Broadhurst, Table of n, A352336(n), A352359(n) for n = 1..221

Example

The initial terms of A109812 and the smallest missing numbers (smn):
  n a(n) smn
  1  1   2
  2  2   3
  3  4   3
  4  3   5
  5  8   5
  6  5   6
  7  10  6
  8  16  6
  9   6  7
  10  9  7
  11  18 7
  12  12 7
  ...
so the distinct smallest missing numbers are 1, 2, 3, 5, 6, 7, ...

Mathematica

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]]

Crossrefs

Cf. A109812, A113233, A352203, A352359.

Sequence in context: A377201 A062101 A330597 * A283599 A096530 A299157

Adjacent sequences: A352333 A352334 A352335 * A352337 A352338 A352339

Keyword

nonn,base

Author

Michael De Vlieger, Mar 29 2022

Extensions

Edited by N. J. A. Sloane, Apr 26 2022 and May 03 2024

Status

approved