A207672 - OEIS

A207672

n + [ns/r] + [nt/r], where []=floor, r=5, s=(1+sqrt(5))/2, t=1/s.

1, 2, 3, 5, 6, 7, 9, 10, 12, 14, 15, 16, 18, 19, 20, 22, 24, 25, 27, 28, 29, 31, 32, 33, 36, 37, 38, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 54, 55, 56, 59, 60, 61, 63, 64, 65, 67, 68, 70, 72, 73, 74, 76, 77, 78, 80, 82, 83, 85, 86, 87, 89, 90, 91, 94, 95, 96, 98

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OFFSET

1,2

COMMENTS

The sequences A207672, A207673, A208326 partition the positive integers. To generate them, jointly rank the sets {i/r}, {j/s}, {k*s}. The positions of n/r in the joint ranking form A207672, and likewise for the other sequences.

For a guide to related sequences and a conjecture, see A206911.

Adamczewski provides a proof abstract regarding the above conjecture in linked article. - Michael De Vlieger, Aug 19 2026

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Tom Adamczewski, OEIS Open: How many conjectures can language models turn into theorems?, arXiv:2608.11941 [cs.AI], 2026. See p. 17 (proof, Appendix A).

MATHEMATICA

r = 5; s = GoldenRatio; t = 1/s;

a[n_] := n + Floor[n*s/r] + Floor[n*t/r];

b[n_] := n + Floor[n*r/s] + Floor[n*t/s];

c[n_] := n + Floor[n*r/t] + Floor[n*s/t];

Table[a[n], {n, 1, 60}] (* A207672 *)

Table[b[n], {n, 1, 60}] (* A207673 *)