A343878 a(n) is the least k such that A342585(k) = n.

1, 2, 5, 9, 11, 21, 25, 30, 47, 39, 59, 71, 96, 100, 126, 115, 160, 178, 197, 217, 221, 261, 243, 265, 336, 322, 374, 419, 397, 479, 425, 485, 551, 583, 649, 618, 723, 653, 801, 690, 727, 887, 930, 974, 889, 932, 1115, 976, 1260, 1310, 1023, 1414, 1070, 1522

Offset: 0

Author

Rémy Sigrist, May 02 2021

Keywords

• nonn
• look
• easy

Comments

The term after the n-th 0 in A342585 is the running total of 0's, and there are infinitely many 0's, so all nonnegative integers appear in A342585. - Peter Munn, May 08 2021

Examples

			We have:
n:       1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21
A342585: 0, 1, 1, 0, 2, 2, 2, 0, 3, 2,  4,  1,  1,  0,  4,  4,  4,  1,  4,  0,  5
So:
- a(0) = 1, a(1) = 2, a(2) = 5, a(3) = 9, a(4) = 11, a(5) = 21.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, PARI program for A343878

Crossrefs

Cf. A342585, A343880.

For records see A347305.

Programs

Mathematica

Block[{a, c, k, m, nn = 54}, c[0] = 1; a = {0}~Join~Reap[Do[k = 0; While[IntegerQ[c[k]], Set[m, c[k]]; Sow[m]; If[IntegerQ@ c[m], c[m]++, c[m] = 1]; k++]; Sow[0]; c[0]++, nn]][[-1, -1]]; TakeWhile[Array[FirstPosition[a, #][[1]] &, nn, 0], IntegerQ]] (* Michael De Vlieger, Oct 12 2021 *)

PARI

See Links section.

Python

def A343878(n):
    k, c = 0, dict()
    while True:
        m, r = 0, 1
        while r > 0:
            k += 1
            r = c.get(m,0)
            if n == r:
                return k
            c[r] = c.get(r,0)+1
            m += 1 # Chai Wah Wu, Aug 31 2021

Formula

For n >= 1, a(n) <= A343880(n) + 1. - Peter Munn, May 08 2021

Extensions

Name shortened by Peter Munn, May 08 2021