A385114 a(n) is the least k with k > a(n-1) such that A000120(k) = A002487(n), with a(0) = 0.

0, 1, 2, 3, 4, 7, 9, 11, 16, 23, 25, 31, 33, 47, 49, 51, 64, 79, 83, 127, 131, 255, 271, 319, 320, 351, 355, 383, 385, 415, 417, 419, 512, 543, 551, 767, 771, 2047, 2111, 2559, 2561, 3071, 3135, 8191, 8207, 10239, 10271, 10367, 12288, 12415, 12431, 13311, 13315, 14335

Offset: 0

Author

Karl-Heinz Hofmann, Jun 18 2025

Keywords

• nonn
• base

Examples

			  n |  a(n)_2   a(n)   A002487(n)
----+-----------------------------
  0 |       0     0       0
  1 |       1     1       1
  2 |      10     2       1
  3 |      11     3       2
  4 |     100     4       1
  5 |     111     7       3
  6 |    1001     9       2
  7 |    1011    11       3
  8 |   10000    16       1
  9 |   10111    23       4
 10 |   11001    25       3
 11 |   11111    31       5
 12 |  100001    33       2
 13 |  101111    47       5
 14 |  110001    49       3
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 0..10000. (Terms 0..293 from Hugo Pfoertner.)
• Karl-Heinz Hofmann, Python code.
• Michael De Vlieger, Plot the i-th bit of a(n) at (x,y) = (n,i), n = 1..2^11, reading bits from the least significant to the most.
• Karl-Heinz Hofmann, Vertical visualization of terms in binary, reading bits from the most significant to the least.

Crossrefs

Cf. A000120, A002487, A101624, A168081, A277020.

Cf. A212288, A212289.

Programs

Mathematica

k = s[0] = 0; s[1] = 1; s[n_] := s[n] = If[EvenQ[n], s[n/2], s[(n - 1)/2] + s[(n + 1)/2]]; Array[s, 2^10]; {k}~Join~Monitor[Table[Set[k, Max[k + 1, 2^s[n] - 1]]; While[DigitCount[k, 2, 1] != s[n], k++]; k, {n, 100}], n] (* Michael De Vlieger, Jul 14 2025 *)

PARI

lista(nn) = my(list = List([0]), last = 0); for (n=1, nn, my(k=last+1, d=dia(n)); while (hammingweight(k) != d, k++); last = k; listput(list, k);); Vec(list); \\ Michel Marcus, Jul 12 2025

Python

# see links

Formula

a(A212288(n)) >= 2^A212289(n+1) - 1. - Hugo Pfoertner, Jul 15 2025