A358049 a(1) = 2, a(2) = 3; afterwards a(n) is least new prime > a(n-1) such that a(n-2) + a(n) and a(n-1) + a(n) are semiprimes.

2, 3, 7, 19, 67, 127, 151, 271, 463, 823, 883, 991, 1051, 1087, 2011, 2251, 2311, 2371, 2383, 2731, 2803, 2971, 3271, 3391, 3643, 3823, 4111, 4483, 6343, 6379, 6763, 7879, 8443, 9199, 9283, 9643, 10159, 10639, 10867, 10939, 11047, 11299, 11467, 11587, 11971, 12511, 12583, 14071

Offset: 1

Author

Zak Seidov, Oct 27 2022

Keywords

• nonn

Comments

Aside from the first two terms, all terms are 7 mod 12. - Charles R Greathouse IV, Dec 07 2022

Examples

			2 + 7 = 9 = 3*3 and 3 + 7 = 10 = 2*5 are semiprimes.
		

Crossrefs

Cf. A001358.

Aside from the first two terms, a subsequence of A068229.

Programs

Mathematica

Do[While[MemberQ[s, p] || 2 != PrimeOmega[s[[-2]] + p] || 2 != PrimeOmega[s[[-1]] + p], p = NextPrime[p]]; AppendTo[s, p], {60}]; s

PARI

issp(n) = bigomega(n) == 2; \\ A001358
lista(nn) = my(va = vector(nn)); va[1] = 2; va[2] = 3; for (n=3, nn, my(p=nextprime(va[n-1]+1)); while (!issp(va[n-2]+p) || !issp(va[n-1]+p), p = nextprime(p+1)); va[n] = p;); va; \\ Michel Marcus, Nov 14 2022