A390295 - OEIS

%I #22 Dec 17 2025 16:29:08

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

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

%C a(10) > 10^12, if it exists. - _Amiram Eldar_, Dec 05 2025

%o (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];

%o (PARI) isok(k) = isprime(k-1) && isprime(k+1) && (sumdiv(k, d, gcd(d^2 - 4, k)==1) == 1); \\ _Michel Marcus_, Dec 03 2025

%o (PARI) is1(k) = {my(c = 0); fordiv(k, d, if(gcd(d^2 - 4, k) == 1, c++; if(c > 1, return(0)))); c == 1;}

%o 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

%Y Cf. A002472, A014574.

%K nonn,more

%O 1,1

%A _Juri-Stepan Gerasimov_, Dec 02 2025