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

Author

Michael De Vlieger, Mar 29 2022

Keywords

• nonn
• base

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

Examples

			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, ...
		

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

Crossrefs

Cf. A109812, A113233, A352203, A352359.

Programs

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]]

Extensions

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