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

Author

Farideh Firoozbakht, May 29 2010

Keywords

• base
• nonn

Comments

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

Examples

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

Crossrefs

Cf. A007954, A178327.

Programs

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 *)

Extensions

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

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