A345707 Primes prime(k) at which A345706(k) attains a record value.

2, 5, 11, 13, 19, 41, 47, 67, 89, 149, 211, 331, 433, 677, 859, 1301

Offset

1,1

Comments

The corresponding records values are 1, 2, 3, 6, 12, 20, 24, 58, 322, 414, 483, 527, 1065, 2597, 3181, 6022, ...

Links

Table of n, a(n) for n=1..16.

Example

The first 6 terms of A345706 are 1, 1, 2, 2, 3 and 6. The record values, 1, 2, 3 and 6, occur at k = 1, 3, 5 and 6. The corresponding primes are prime(k) = 2, 5, 11 and 13, the first 4 terms of this sequence.

Mathematica

f[n_] := Module[{r = Product[Prime[j], {j, 1, n - 1}], p = Prime[n], k}, k = Max[1, Ceiling@Log[p, r]]; While[! PrimeQ[r*p^k + 1], k++]; k]; fm = 0; s = {}; Do[f1 = f[k]; If[f1 > fm, fm = f1; AppendTo[s, Prime[ k]]], {k, 1, 50}]; s

Crossrefs

Cf. A053341, A345706.

Sequence in context: A045361 A276660 A086081 * A113305 A095078 A335874

Adjacent sequences: A345704 A345705 A345706 * A345708 A345709 A345710

Keyword

nonn,more

Author

Amiram Eldar, Jun 24 2021

Status

approved