A133478 a(n) = smallest semiprime s such that s + n is the next semiprime and there is no prime between s and s + n.

9, 49, 62, 403, 341, 843, 6722, 3473, 2869, 14059, 18467, 26603, 166126, 41779, 74491, 192061, 463161, 226489, 344119, 517421, 943606, 2171131, 4577519, 584213, 2560177, 4356633, 8367139, 11174753, 13191293, 7319797, 27841051, 10644122, 13683034, 29492893, 47735342, 26837363, 63305661, 90455097, 189662206, 120175651

Offset: 1

Author

Jack Brennen and Zak Seidov, Dec 23 2007

Keywords

• nonn

Examples

			a(1)=9 because there is no prime between 9 and 10.
a(2)=49 because there is no prime between 49 and 51.
a(3)=62 because there is no prime between 62 and 65.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..60.

Programs

Mathematica

nn = 20; sp1 = 4; t = Table[0, {nn}]; found = 0; fQ[s_] := Union@ PrimeQ[s] == {False}; NextSemiPrime[n_, k_: 1] := Block[{c = 0, sgn = Sign[k]}, sp = n + sgn; While[c < Abs[k], While[ PrimeOmega[sp] != 2, If[sgn < 0, sp--, sp++]]; If[ sgn < 0, sp--, sp++]; c++]; sp + If[sgn < 0, 1, -1]]; While[found < nn, sp2 = NextSemiPrime[sp1]; d = sp2 - sp1; If[d <= nn && t[[d]] == 0 && fQ[Range[sp1, sp2]], t[[d]] = sp1; found++; Print[{d, sp1}]]; sp1 = sp2]; t (* Robert G. Wilson v, Jun 13 2013 *)

Extensions

a(37)-a(40) from Jacques Tramu, Dec 23 2007