A174798 Numbers n such that 2*prime(n) and 2*prime(n+1) are consecutive semiprimes.

1, 3, 10, 33, 43, 49, 50, 57, 63, 100, 113, 120, 131, 140, 149, 159, 173, 195, 206, 224, 230, 277, 284, 303, 315, 320, 332, 366, 373, 394, 395, 401, 448, 463, 469, 471, 473, 477, 483, 484, 492, 513, 524, 530, 534, 537, 543, 555, 558, 576, 577, 592, 600, 608

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 29 2010

Keywords

• nonn

Comments

There are no semiprimes strictly between 2*prime(n) and 2*prime(n+1).

A174956(A100484(a(n+1)))=A174956(A100484(a(n)))+1. [From Reinhard Zumkeller, Apr 03 2010]

Examples

			a(1)=1 because 2*prime(1)=4=semiprime(1) and 2*prime(1+1)=6=semiprime(2).
a(2)=3 because 2*prime(3)=10=semiprime(4) and 2*prime(3+1)=14=semiprime(5).
		

Crossrefs

Cf. A000040, A001358, A174797.

Programs

Mathematica

PrimePi[First[#]]&/@Select[Partition[Select[Range[20000],PrimeOmega[#] == 2&], 2,1]/2,And@@IntegerQ/@#&] (* Harvey P. Dale, Nov 19 2011 *)

Formula

A000040(a(n)) = A001358(A174797(n))/2.

Extensions

Edited, corrected and extended by Ray Chandler, Apr 07 2010