A261371 Prime numbers that sum to a prime when added to their digital root.

11, 13, 29, 53, 67, 71, 89, 101, 103, 137, 191, 193, 227, 229, 233, 269, 281, 359, 431, 449, 461, 463, 499, 569, 593, 641, 643, 659, 683, 701, 719, 769, 821, 823, 857, 859, 877, 967, 1019, 1061, 1091, 1093, 1223, 1289, 1439, 1451, 1487, 1489, 1579, 1597, 1601, 1619

Offset: 1

Author

Gary Croft, Sep 11 2015

Keywords

• nonn
• base

Examples

			11 (prime) + 2 (its digital root) = 13 (prime);
89 (prime) + 8 (its digital root) = 97 (prime).
		

Crossrefs

Cf. A000040, A010888, A038194.

Programs

Magma

[p: p in PrimesUpTo(2000) | IsPrime(p+(p mod 9))]; // Vincenzo Librandi, Sep 29 2015

Mathematica

Select[Prime[Range[300]], PrimeQ[# + Mod[#, 9]] &] (* Vincenzo Librandi, Sep 29 2015 *)

PARI

lista(nn) = forprime(p=2, nn, if (isprime(p + p%9), print1(p, ", "))); \\ Michel Marcus, Sep 12 2015

Formula

(a(n) mod 9) mod 2 = 0. - Altug Alkan, Sep 28 2015