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A174798 Numbers n such that 2*prime(n) and 2*prime(n+1) are consecutive semiprimes. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 8 07:02 EDT 2021. Contains 343653 sequences. (Running on oeis4.)