A264045 Numbers n such that n and n+5 are consecutive semiprimes.

69, 77, 106, 161, 178, 221, 254, 309, 314, 329, 341, 386, 398, 417, 422, 473, 554, 662, 674, 689, 758, 794, 934, 974, 998, 1094, 1121, 1149, 1169, 1214, 1294, 1502, 1517, 1522, 1541, 1569, 1673

Offset: 1

Author

Zak Seidov, Nov 02 2015

Keywords

• nonn

Comments

Note that a(1)=69=A131109(k=5).

Examples

			a(1)=69=A001358(24) and a(1)+k=74=A001358(25).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A065516, A123375, A131109, A136196, A264043, A264044.

Programs

Mathematica

Flatten[Position[Partition[Table[If[PrimeOmega[n]==2,1,0],{n,2000}],6,1], ?(#=={1,0,0,0,0,1}&)]] (* _Harvey P. Dale, Dec 16 2015 *)

PARI

is(n)=if(n%4==1, isprime((n+5)/2) && bigomega(n)==2, n%4==2 && isprime(n/2) && bigomega(n+5)==2) && bigomega(n+1)!=2 && bigomega(n+2)!=2 && bigomega(n+3)!=2 && bigomega(n+4)!=2 \\ Charles R Greathouse IV, Nov 02 2015

Formula

a(n) >> n log n. - Charles R Greathouse IV, Nov 02 2015