A241809 Semiprimes sp such that sp+2 is a prime.

9, 15, 21, 35, 39, 51, 57, 65, 69, 77, 87, 95, 111, 129, 155, 161, 177, 209, 221, 237, 249, 267, 291, 305, 309, 329, 335, 365, 371, 377, 381, 395, 407, 417, 437, 447, 485, 489, 497, 501, 519, 545, 591, 597, 611, 629, 671, 681, 689, 699, 707, 717, 731, 737, 749

Offset: 1

Author

K. D. Bajpai, Apr 29 2014

Keywords

• nonn
• easy

Examples

			a(2) = 15 = 3*5, which is semiprime and 15+2 = 17 is a prime.
a(6) = 51 = 3*17, which is semiprime and 51+2 = 53 is a prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..1370

Crossrefs

Cf. A001358, A062721, A063638, A107986.

Programs

Maple

with(numtheory): A241809:= proc(); if bigomega(x)=2 and isprime(x+2)then  RETURN (x); fi; end: seq(A241809 (), x=1..2000);

Mathematica

A241809={};Do[If[PrimeOmega[n]==2&&PrimeQ[n+2],AppendTo[A241809,n]],{n,1000}];A241809
Select[Prime[Range[200]]-2,PrimeOmega[#]==2&] (* Harvey P. Dale, Aug 06 2015 *)
SequencePosition[Table[Which[PrimeQ[n],1,PrimeOmega[n]==2,2,True,0],{n,800}],{2,,1}][[;;,1]] (* _Harvey P. Dale, Oct 05 2023 *)

PARI

for(k=1, 1000, if(bigomega(k)==2 && isprime(k+2), print1(k, ", "))) \\ Colin Barker, May 07 2014

Formula

a(n) = A063638(n) - 2.