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

%I A214629 #23 May 08 2021 07:50:33
%S A214629 11,13,19,23,29,31,37,43,53,59,61,73,79,89,97,101,223,263,283,401,409,
%T A214629 443,601,607,809,823,829,883,1013,1019,1031,1033,1039,1051,1091,1093,
%U A214629 1097,1103,1109,1117,1123,1129,1151,1163,1171,1181,1187,1193,1213,1231,1259
%N A214629 Primes p such that the sum of the digits plus the product of the digits is a prime.
%H A214629 Robert Israel, <a href="/A214629/b214629.txt">Table of n, a(n) for n = 1..10000</a>
%F A214629 {p in A000040: A061762(p) in A000040}. - _R. J. Mathar_, Aug 13 2012
%e A214629 11 is in the sequence because A061762(11) = 3 is prime.
%p A214629 f:= proc(n) local L;
%p A214629    L:= convert(n,base,10);
%p A214629    convert(L,`+`)+convert(L,`*`)
%p A214629 end proc:
%p A214629 select(p -> isprime(f(p)), [seq(ithprime(i),i=1..1000)]); # _Robert Israel_, May 07 2021
%t A214629 f[n_] := Module[{in = IntegerDigits[n]}, Times @@ in + Plus @@ in];Select[Prime[Range[300]], PrimeQ[f[#]] &]
%Y A214629 Cf. A061762, A344032. Primes in A185300.
%K A214629 nonn,base
%O A214629 1,1
%A A214629 _Vicente Izquierdo Gomez_, Aug 13 2012