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

1,1

Comments

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

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A325386 A260428 A168477 * A295806 A210614 A235226

Adjacent sequences: A264042 A264043 A264044 * A264046 A264047 A264048

Keyword

nonn

Author

Zak Seidov, Nov 02 2015

Status

approved