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

Author

Zak Seidov, Sep 03 2009

Keywords

• nonn
• more
• hard

Comments

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

Crossrefs

Subsequence of A045375.

Cf. A001358, A114845, A116656.

Programs

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

Formula

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

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

Extensions

a(12) from Amiram Eldar, Jun 27 2024

a(13) from Jinyuan Wang, May 29 2025