A067464 Primes p such that sigma(p-1)+sigma(p+1) is prime.

2, 5, 37, 101, 257, 401, 4801, 12101, 22501, 25537, 25601, 31249, 33857, 160001, 217157, 401957, 404497, 476101, 512657, 583697, 1020101, 1270417, 1322501, 1503377, 1674437, 1943237, 2005057, 2016401, 2056357, 2689601, 2755601, 2842597, 3686401, 3920401

Offset: 1

Author

Benoit Cloitre, Feb 23 2002

Keywords

• nonn

Examples

			401 is here as 401 is prime and sigma(401 - 1) + sigma(401 + 1) = 961 + 816 = 1777 which is prime. - _David A. Corneth_, Feb 17 2021
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 150 terms from Hagen v. Eitzen)

Crossrefs

Cf. A028982.

Programs

Mathematica

Select[Prime[Range[300000]],PrimeQ[DivisorSigma[1,#-1]+DivisorSigma[ 1, #+1]]&] (* Harvey P. Dale, Jul 13 2018 *)

PARI

isok(p) = isprime(p) && isprime(sigma(p-1)+sigma(p+1)); \\ Michel Marcus, Feb 17 2021

PARI

upto(n) = {my(res = List()); for(i = 1, sqrtint(n + 1), if(isprime(2*i^2 - 1) && isprime(sigma(2*i^2-2) + sigma(2*i^2)) && 2*i^2 - 1 <= n, listput(res, 2*i^2 - 1); ); if(isprime(i^2 + 1) && isprime(sigma(i^2) + sigma(i^2 + 2)), listput(res, i^2 + 1); ) ); Set(res) } \\ David A. Corneth, Feb 17 2021

Extensions

More terms from Sascha Kurz, Mar 18 2002