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

1,2

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]

Links

Table of n, a(n) for n=1..54.

Formula

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

Example

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).

Mathematica

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

Crossrefs

Cf. A000040, A001358, A174797.

Sequence in context: A149028 A174573 A126183 * A042039 A080697 A316404

Adjacent sequences: A174795 A174796 A174797 * A174799 A174800 A174801

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 29 2010

Extensions

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

Status

approved