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Numbers k such that k^p+p is prime, where p is product of the digits of k.
1

%I #14 Jun 23 2023 09:51:32

%S 1,21,6617,12131,12441,114917,121221,124281,125121,145581,172631,

%T 182121,191213,211551,221211,221421,241213,293143,421531,421821

%N Numbers k such that k^p+p is prime, where p is product of the digits of k.

%C All terms are odd. Large numbers corresponding to some terms are probable

%C prime. There is no further term up to 27500.

%C 254597 < a(18) <= 293143. a(19) <= 421531. a(20) <= 421821. - _Donovan Johnson_, Aug 09 2010

%e 21^(2*1)+(2*1) is prime so 21 is a term.

%t Do[p=Apply[Times, IntegerDigits[n]]; If[PrimeQ[n^p+p], Print[n]],

%t {n, 1, 27501, 2}]

%Y Cf. A178328, A099227.

%K base,more,nonn

%O 1,2

%A _Farideh Firoozbakht_, May 29 2010

%E No more terms less than 56600. - _Robert G. Wilson v_, Jul 27 2010

%E a(6)-a(17) from _Donovan Johnson_, Aug 09 2010

%E a(18)-a(20) from _Michael S. Branicky_, Jun 23 2023