A390295 Average k of twin prime pairs such that gcd(d^2 - 4, k) = 1 for only one divisor d of k.

4, 6, 12, 30, 60, 192, 240, 15360, 786432

Offset

1,1

Comments

a(10) > 10^12, if it exists. - Amiram Eldar, Dec 05 2025

Links

Table of n, a(n) for n=1..9.

Prog

(Magma) [k: k in [1..10^6] | IsPrime(k-1) and IsPrime(k+1) and #[d: d in Divisors(k) | Gcd(d^2-4, k) eq 1] eq 1];
(PARI) isok(k) = isprime(k-1) && isprime(k+1) && (sumdiv(k, d, gcd(d^2 - 4, k)==1) == 1); \\ Michel Marcus, Dec 03 2025
(PARI) is1(k) = {my(c = 0); fordiv(k, d, if(gcd(d^2 - 4, k) == 1, c++; if(c > 1, return(0)))); c == 1; }
list(kmax) = {my(q = 3); forprime(p = 5, kmax+1, if(p == q + 2 && is1(q+1), print1(q+1, ", ")); q = p); } \\ Amiram Eldar, Dec 05 2025

Crossrefs

Cf. A002472, A014574.

Sequence in context: A375197 A056495 A351523 * A263656 A178674 A025018

Adjacent sequences: A390292 A390293 A390294 * A390296 A390297 A390298

Keyword

nonn,more

Author

Juri-Stepan Gerasimov, Dec 02 2025

Status

approved