A356309 The least j >= n such that n and A276086(j) are relatively prime, where A276086 is the primorial base exp-function.

0, 1, 2, 6, 4, 5, 6, 7, 8, 12, 30, 11, 12, 13, 14, 30, 16, 17, 18, 19, 30, 24, 22, 23, 24, 30, 26, 30, 28, 29, 30, 31, 32, 36, 34, 210, 36, 37, 38, 42, 60, 41, 210, 43, 44, 60, 46, 47, 48, 210, 60, 54, 52, 53, 54, 60, 210, 60, 58, 59, 60, 61, 62, 210, 64, 65, 66, 67, 68, 72, 210, 71, 72, 73, 74, 90, 76, 2310, 78

Offset: 0

Author

Antti Karttunen, Nov 04 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..11550
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
• Index entries for sequences related to primorial base

Crossrefs

Cf. A276086, A356302, A356313.

Cf. A324583 (positions of the fixed points), A356314 (positions of the terms that are primorial numbers), A356316 (where a(n) is a multiple of n), A356318 (where a nontrivial multiple), A356319 (where n < a(n) < 2*n).

Programs

Mathematica

f[nn_] := Block[{m = 1, i = 1, n = nn, p}, While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; m]; Array[Block[{k = #}, While[! CoprimeQ[#, f[k]], k++]; k] &, 79, 0] (* Michael De Vlieger, Nov 06 2022, after Jean-François Alcover at A276086 *)

PARI

A356309(n) = (n+A356302(n)); \\ See code in the latter sequence.

Formula

a(n) = n + A356302(n).