A217836 a(n) is largest semiprime < 2*a(n-1), with a(1) = 4.

4, 6, 10, 15, 26, 51, 95, 187, 371, 737, 1473, 2942, 5878, 11755, 23507, 47013, 94021, 188041, 376069, 752135, 1504261, 3008503, 6017001, 12034001, 24068001, 48135995, 96271987, 192543973, 385087943, 770175883, 1540351763, 3080703523, 6161407045, 12322814089, 24645628171

Offset: 1

Author

Jonathan Vos Post, Oct 19 2012

Keywords

• nonn
• easy

Comments

This is to Bertrand primes A006992 as semiprimes A001358 are to primes A000040.

Examples

			a(2) = 6 because that is the largest semiprime < 2*a(1) = 8, where a(1) is the first semiprime.
a(3) = 10, the largest semiprime < 2*6 = 12.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1...225

Crossrefs

Cf. A001358, A006992.

Programs

Mathematica

PrevSemiPrime[n_, k_] := Block[{c = 0, sp = n - 1}, While[c < k, While[ PrimeOmega[sp] != 2, sp--]; sp--; c++]; sp + 1]; NestList[ PrevSemiPrime[ 2#, 1] &, 4, 34] (* Robert G. Wilson v, Oct 19 2012 *)

Extensions

Terms greater than a(15) from Robert G. Wilson v, Oct 19 2012