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Numbers k such that prime(k)-2 and prime(k+2)-2 are both primes.
6

%I #12 Oct 04 2024 06:56:13

%S 4,6,27,34,42,44,82,141,143,172,177,235,287,295,314,319,429,459,474,

%T 476,485,578,580,585,672,744,773,863,871,873,892,935,958,1031,1116,

%U 1166,1168,1170,1231,1340,1352,1405,1463,1549,1622,1652,1708,1824,1834,1868

%N Numbers k such that prime(k)-2 and prime(k+2)-2 are both primes.

%H Amiram Eldar, <a href="/A105409/b105409.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI) pnpk(n, m=2, 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

%o (PARI) lista(pmax) = {my(k = 1, p = primes(4)); forprime(p1 = p[#p], pmax, k++; p[#p] = p1; if(p[2]- p[1] == 2 && p[4] - p[3] == 2, print1(k, ", ")); for(i = 1, #p-1, p[i] = p[i+1]));} \\ _Amiram Eldar_, Oct 04 2024

%Y Cf. A053778, A105410, A105411, A105412, A105413, A105414.

%K nonn

%O 1,1

%A _Cino Hilliard_, May 01 2005

%E Offset corrected by _Amiram Eldar_, Oct 04 2024