A214629 Primes p such that the sum of the digits plus the product of the digits is a prime.

11, 13, 19, 23, 29, 31, 37, 43, 53, 59, 61, 73, 79, 89, 97, 101, 223, 263, 283, 401, 409, 443, 601, 607, 809, 823, 829, 883, 1013, 1019, 1031, 1033, 1039, 1051, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1163, 1171, 1181, 1187, 1193, 1213, 1231, 1259

Offset: 1

Author

Vicente Izquierdo Gomez, Aug 13 2012

Keywords

• nonn
• base

Examples

			11 is in the sequence because A061762(11) = 3 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A061762, A344032. Primes in A185300.

Programs

Maple

f:= proc(n) local L;
   L:= convert(n,base,10);
   convert(L,`+`)+convert(L,`*`)
end proc:
select(p -> isprime(f(p)), [seq(ithprime(i),i=1..1000)]); # Robert Israel, May 07 2021

Mathematica

f[n_] := Module[{in = IntegerDigits[n]}, Times @@ in + Plus @@ in];Select[Prime[Range[300]], PrimeQ[f[#]] &]

Formula

{p in A000040: A061762(p) in A000040}. - R. J. Mathar, Aug 13 2012