A176652 Numbers k such that both semiprime(k)/p and semiprime(k+1)/p are prime for some prime p.

1, 2, 4, 6, 21, 42, 87, 120, 141, 142, 168, 179, 185, 188, 245, 255, 320, 363, 387, 434, 464, 496, 539, 593, 675, 697, 721, 753, 794, 810, 894, 929, 995, 1023, 1032, 1060, 1080, 1081, 1105, 1147, 1166, 1221, 1224, 1228, 1275, 1356, 1391, 1477, 1478, 1498

Offset

1,2

Comments

Indices n such that A001358(n) and A001358(n+1) share one prime factor. - R. J. Mathar, Apr 26 2010

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

2 is a term because both semiprime(2)/3 = 6/3 = 2 and semiprime(2+1)/3 = 9/3 = 3 are prime.

Maple

isA176652 := proc(n) pfsn := convert(numtheory[factorset]( A001358(n) ), list) ; pfsn1 := convert(numtheory[factorset]( A001358(n+1) ), list) ; op(1, pfsn) = op(1, pfsn1) or op(1, pfsn) = op(-1, pfsn1) or op(-1, pfsn) = op(1, pfsn1) or op(-1, pfsn) = op(-1, pfsn1) ; end proc: for n from 1 to 1600 do if isA176652(n) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, Apr 26 2010

Mathematica

sppQ[{a_, b_}]:=Module[{af=FactorInteger[a][[All, 1]], bf=FactorInteger[b][[All, 1]]}, Length[Intersection[af, bf]]==1]; Position[Partition[ Select[ Range[7000], PrimeOmega[#]==2&], 2, 1], _?sppQ]//Flatten (* Harvey P. Dale, Oct 08 2017 *)

Crossrefs

Cf. A001358.

Sequence in context: A193774 A241210 A333992 * A251724 A326363 A273522

Adjacent sequences: A176649 A176650 A176651 * A176653 A176654 A176655

Keyword

nonn

Author

Juri-Stepan Gerasimov, Apr 22 2010

Extensions

Extended beyond 141 by R. J. Mathar, Apr 26 2010

Name clarified by Jon E. Schoenfield, Feb 06 2019

Status

approved