A342961 Primes p such that p + the sum of its prime digits is prime.

11, 19, 29, 37, 41, 53, 61, 73, 89, 101, 109, 149, 181, 191, 199, 229, 233, 257, 269, 277, 281, 307, 331, 359, 379, 383, 401, 409, 419, 433, 449, 461, 491, 499, 563, 587, 593, 601, 619, 641, 653, 661, 673, 677, 691, 727, 797, 809, 811, 821, 881, 911, 919, 937, 941, 977, 991, 1009, 1019, 1033

Offset: 1

Author

J. M. Bergot and Robert Israel, Mar 31 2021

Keywords

• nonn
• base

Examples

			a(3) = 29 is a term because it is prime, the sum of its prime digits is 2, and 29+2 = 31 is also prime.
		

Links

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

Crossrefs

Includes A034844. Cf. A085563, A342962.

Programs

Maple

f:= p -> p + convert(select(isprime,convert(p,base,10)),`+`):
select(t -> isprime(t) and isprime(f(t)), [seq(i,i=3..2000,2)]);

Mathematica

Select[Prime@Range@200,PrimeQ@Total[Join[{#},Select[IntegerDigits@#,PrimeQ]]]&] (* Giorgos Kalogeropoulos, Apr 01 2021 *)

PARI

isok(p) = isprime(p) && isprime(p+sumdigits(p)); \\ Michel Marcus, Apr 01 2021