A178328 Numbers k such that k^p-p is prime, where p is product of the digits of k.

2, 21, 121, 211, 223, 631, 1211, 1663, 1811, 1831, 2127, 2813, 4211, 5497, 6211, 8411, 12149, 12287, 18113, 19121, 23311, 24113, 24311, 27311, 31651, 32129, 32221, 34171, 38131, 41213, 47231, 49183, 53831, 56831, 111223, 111421, 111811, 121279, 123121, 129151, 141233, 156271, 157651, 161171

Offset

1,1

Comments

2 is the only even term of this sequence. Large numbers corresponding to some terms are probable prime.

Links

Table of n, a(n) for n=1..44.

Example

21^(2*1) - (2*1) is prime so 21 is in the sequence.

Mathematica

Do[p=Apply[Times, IntegerDigits[n]]; If[PrimeQ[n^p-p], Print[n]], {n, 54891}]
(* or *)
ppdQ[n_]:=Module[{p=Times@@IntegerDigits[n]}, PrimeQ[n^p-p]]; Select[ Range[ 120000], ppdQ] (* Harvey P. Dale, Nov 12 2017 *)

Crossrefs

Cf. A007954, A178327.

Sequence in context: A369754 A068045 A188530 * A091789 A109789 A136588

Adjacent sequences: A178325 A178326 A178327 * A178329 A178330 A178331

Keyword

base,nonn

Author

Farideh Firoozbakht, May 29 2010

Extensions

a(34)-a(37) from Max Alekseyev, Feb 19 2012

a(38)-a(44) from Michael S. Branicky, Jun 25 2023

Status

approved