A358049 - OEIS

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.

%I #18 Dec 07 2022 15:00:26

%S 2,3,7,19,67,127,151,271,463,823,883,991,1051,1087,2011,2251,2311,

%T 2371,2383,2731,2803,2971,3271,3391,3643,3823,4111,4483,6343,6379,

%U 6763,7879,8443,9199,9283,9643,10159,10639,10867,10939,11047,11299,11467,11587,11971,12511,12583,14071

%N 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.

%C Aside from the first two terms, all terms are 7 mod 12. - _Charles R Greathouse IV_, Dec 07 2022

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

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

%o (PARI) issp(n) = bigomega(n) == 2; \\ A001358

%o 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

%Y Cf. A001358.

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

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 27 2022