A264044 Numbers n such that n and n+4 are consecutive semiprimes.

10, 51, 58, 65, 87, 111, 129, 209, 249, 274, 291, 305, 335, 377, 382, 403, 407, 447, 454, 485, 489, 493, 497, 529, 538, 629, 681, 699, 713, 749, 767, 781, 785, 803, 831, 889, 901, 917, 939, 951, 961, 985, 989, 1007, 1037, 1073, 1115, 1191, 1207

Offset

1,1

Comments

Note that a(1)=10=A131109(k=4).

Subsequence of A175648: a(1)=10=A175648(2), a(2)=51=A175648(7), a(3)=58=A175648(8), etc. - Zak Seidov, Dec 20 2017

Links

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

Example

10=A001358(4) and 14=A001358(5).

Maple

B:= select(numtheory:-bigomega=2, [$1..2000]):
B[select(t ->B[t+1]-B[t]=4, [$1..nops(B)-1])]; # Robert Israel, Dec 21 2017

Mathematica

Select[Partition[Select[Range[1250], PrimeOmega@ # == 2 &], 2, 1], Differences@ # == {4} &][[All, 1]] (* Michael De Vlieger, Dec 20 2017 *)
SequencePosition[Table[If[PrimeOmega[n]==2, 1, 0], {n, 1300}], {1, 0, 0, 0, 1}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 19 2020 *)

Prog

(PARI) is(n)=bigomega(n)==2 && bigomega(n+4)==2 && bigomega(n+1)!=2 && bigomega(n+2)!=2 && bigomega(n+3)!=2 \\ Charles R Greathouse IV, Nov 02 2015

Crossrefs

Cf. A001358, A065516, A123375, A131109, A136196, A175648, A264043.

Sequence in context: A143558 A106041 A370737 * A143855 A124162 A077044

Adjacent sequences: A264041 A264042 A264043 * A264045 A264046 A264047

Keyword

nonn

Author

Zak Seidov, Nov 02 2015

Status

approved