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

1,1

Comments

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

Links

Table of n, a(n) for n=1..48.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A001358.

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

Sequence in context: A167422 A060276 A337187 * A025563 A336296 A224929

Adjacent sequences: A358046 A358047 A358048 * A358050 A358051 A358052

Keyword

nonn

Author

Zak Seidov, Oct 27 2022

Status

approved