A165138 Smallest prime p > prime(n) such that p+prime(n) is a semiprime.

7, 7, 17, 19, 23, 61, 29, 43, 59, 53, 43, 97, 53, 79, 59, 89, 83, 73, 79, 107, 181, 127, 131, 113, 109, 113, 151, 167, 193, 149, 151, 167, 197, 163, 197, 163, 229, 199, 179, 281, 347, 241, 263, 229, 257, 223, 271, 331, 239, 313, 269, 263, 313, 263, 269, 359, 293

Offset: 1

Author

Zak Seidov, Sep 04 2009

Keywords

• nonn

Comments

Except for having an additional first term the sequence coincides with A084704.

For n>2, a(n)-prime(n) is a multiple of 12, e.g., 17-5, 19-7, 23-11, etc. - Zak Seidov, Oct 15 2015

Examples

			2+7=9=3*3 (semiprime), 3+7=10=2*5 (semiprime), 5+17=22=2*11 (semiprime).
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A084704, A001358, A145471.

Programs

Mathematica

sp[n_]:=Module[{np=NextPrime[n]},While[PrimeOmega[n+np]!=2,np= NextPrime[ np]]; np]; sp/@Prime[Range[60]] (* Harvey P. Dale, Apr 06 2016 *)

PARI

a(n) = {q = prime(n); p = nextprime(q+1); while (bigomega(p+q)!=2, p = nextprime(p+1)); p;} \\ Michel Marcus, Oct 15 2015

Extensions

Prior Mathematica program deleted by Harvey P. Dale, Apr 06 2016