A164979 Slowest growing sequence of primes having the semiprime-pairwise property: for any i,j, a(i)+a(j) is semiprime.

2, 7, 19, 67, 127, 6619, 126127, 345979, 476407, 1658119, 15182459419, 105169832587, 287583971287

Offset

1,1

Comments

By Dirichlet's theorem and Linnik's theorem, a(n) exists for all n. - Charles R Greathouse IV, Jun 03 2025

Links

Table of n, a(n) for n=1..13.

Formula

a(n) = A114845(n)/2.

a(n) << A070826(n)^5. - Charles R Greathouse IV, Jun 03 2025

Prog

(PARI) lista(pmax) = {my(v = [2], ans); print1(v[1], ", "); forprime(p=3, pmax, ans = 1; for(i=1, #v, if(bigomega(p + v[i]) != 2, ans = 0; break)); if(ans, print1(p, ", "); v=concat(v, p))); } \\ Amiram Eldar, Jun 27 2024

Crossrefs

Subsequence of A045375.

Cf. A001358, A114845, A116656.

Sequence in context: A083309 A380337 A318264 * A243279 A362097 A080873

Adjacent sequences: A164976 A164977 A164978 * A164980 A164981 A164982

Keyword

nonn,more,hard

Author

Zak Seidov, Sep 03 2009

Extensions

a(12) from Amiram Eldar, Jun 27 2024

a(13) from Jinyuan Wang, May 29 2025

Status

approved