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


%S 1,2,4,6,21,42,87,120,141,142,168,179,185,188,245,255,320,363,387,434,

%T 464,496,539,593,675,697,721,753,794,810,894,929,995,1023,1032,1060,

%U 1080,1081,1105,1147,1166,1221,1224,1228,1275,1356,1391,1477,1478,1498

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

%C Indices n such that A001358(n) and A001358(n+1) share one prime factor. - _R. J. Mathar_, Apr 26 2010

%H Harvey P. Dale, <a href="/A176652/b176652.txt">Table of n, a(n) for n = 1..1000</a>

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

%p 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

%t 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 *)

%Y Cf. A001358.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Apr 22 2010

%E Extended beyond 141 by _R. J. Mathar_, Apr 26 2010

%E Name clarified by _Jon E. Schoenfield_, Feb 06 2019

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Last modified December 9 03:27 EST 2019. Contains 329872 sequences. (Running on oeis4.)