A295052 Smallest b > n+2 such that n*b^n + 1 is a generalized Cullen prime with base b > n+2 or 0 if no such prime exists.

4, 6, 10, 0, 8, 14, 30, 12, 14, 132, 42, 143, 60, 30, 22, 170, 30, 665, 198, 42, 200, 138, 104, 115, 34, 84, 0, 1740, 54, 403, 130, 150, 134, 58, 72, 111, 778, 204, 174, 1681, 108, 344, 178, 585, 86, 7426, 924, 133, 234, 63, 1376, 4081, 114, 108, 502, 300, 256, 2596, 180, 2440, 706, 408, 98, 0

Offset

1,1

Comments

No prime found for n = 4, 27, 64 (see A239666).

If A239666(n) = 0, then a(n) = 0. - Michel Marcus, Dec 19 2025

Links

Michel Marcus, Table of n, a(n) for n = 1..300

Mathematica

A097792Q[n_] := (Divisible[n, 4] && IntegerQ[Surd[n/4, 4]]) || Module[{f = FactorInteger[n], s}, AnyTrue[FactorInteger[GCD @@ f[[;; , 2]]][[;; , 1]], # > 2 && IntegerQ[s = Surd[n, #]] && IntegerQ[s/#] &]]; a[n_] := If[A097792Q[n], 0, Module[{b = n + 3}, While[! PrimeQ[n*b^n + 1], b++]; b]]; Array[a, 64] (* Amiram Eldar, Dec 19 2025 *)

Prog

(PARI) a(n) = if (is_A097792(n), 0, my(b=n+3); while (!ispseudoprime(n*b^n + 1), b++); b); \\ Michel Marcus, Dec 18 2025

Crossrefs

Cf. A097792, A239666.

Cf. A210339.

Sequence in context: A115655 A363248 A084350 * A028279 A114743 A089546

Adjacent sequences: A295049 A295050 A295051 * A295053 A295054 A295055

Keyword

nonn

Author

Pierre CAMI, Nov 13 2017

Extensions

a(1) inserted, corrected and extended by Michel Marcus, Dec 19 2025

Status

approved