A105410 Numbers k such that prime(k)-2 and prime(k+3)-2 are both primes.

3, 8, 11, 18, 50, 58, 114, 174, 207, 210, 213, 254, 263, 266, 316, 321, 344, 396, 406, 461, 493, 496, 499, 543, 556, 582, 614, 626, 644, 724, 727, 741, 847, 932, 1099, 1102, 1118, 1121, 1233, 1236, 1261, 1285, 1443, 1616, 1619, 1640, 1705, 1710, 1783, 1792

Offset: 1

Author

Cino Hilliard, May 02 2005

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A105409, A105411, A105412, A105413, A105414.

Programs

Mathematica

Select[Range[2000],PrimeQ[Prime[#]-2]&&PrimeQ[Prime[#+3]-2]&] (* Harvey P. Dale, Jun 02 2011 *)

PARI

pnpk(n, m=3, k=2) = { local(x, v1, v2); for(x=1, n, v1 = prime(x)-k; v2 = prime(x+m)-k; if(isprime(v1)&isprime(v2), print1(x, ", ") ) ) ; } \\ corrected by Amiram Eldar, Oct 04 2024

PARI

lista(pmax) = {my(k = 1, p = primes(5)); forprime(p1 = p[#p], pmax, k++; p[#p] = p1; if(p[2]- p[1] == 2 && p[5] - p[4] == 2, print1(k, ", ")); for(i = 1, #p-1, p[i] = p[i+1]));} \\ Amiram Eldar, Oct 04 2024

Extensions

Offset corrected by Amiram Eldar, Oct 04 2024