A214629 - OEIS

%I #23 May 08 2021 07:50:33

%S 11,13,19,23,29,31,37,43,53,59,61,73,79,89,97,101,223,263,283,401,409,

%T 443,601,607,809,823,829,883,1013,1019,1031,1033,1039,1051,1091,1093,

%U 1097,1103,1109,1117,1123,1129,1151,1163,1171,1181,1187,1193,1213,1231,1259

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

%H Robert Israel, <a href="/A214629/b214629.txt">Table of n, a(n) for n = 1..10000</a>

%F {p in A000040: A061762(p) in A000040}. - _R. J. Mathar_, Aug 13 2012

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

%p f:= proc(n) local L;

%p    L:= convert(n,base,10);

%p    convert(L,`+`)+convert(L,`*`)

%p end proc:

%p select(p -> isprime(f(p)), [seq(ithprime(i),i=1..1000)]); # _Robert Israel_, May 07 2021

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

%Y Cf. A061762, A344032. Primes in A185300.

%K nonn,base

%O 1,1

%A _Vicente Izquierdo Gomez_, Aug 13 2012