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A241809 Semiprimes sp such that sp+2 is a prime. 3

%I #22 Oct 05 2023 16:41:10

%S 9,15,21,35,39,51,57,65,69,77,87,95,111,129,155,161,177,209,221,237,

%T 249,267,291,305,309,329,335,365,371,377,381,395,407,417,437,447,485,

%U 489,497,501,519,545,591,597,611,629,671,681,689,699,707,717,731,737,749

%N Semiprimes sp such that sp+2 is a prime.

%H K. D. Bajpai, <a href="/A241809/b241809.txt">Table of n, a(n) for n = 1..1370</a>

%F a(n) = A063638(n) - 2.

%e a(2) = 15 = 3*5, which is semiprime and 15+2 = 17 is a prime.

%e a(6) = 51 = 3*17, which is semiprime and 51+2 = 53 is a prime.

%p with(numtheory): A241809:= proc(); if bigomega(x)=2 and isprime(x+2)then RETURN (x); fi; end: seq(A241809 (), x=1..2000);

%t A241809={};Do[If[PrimeOmega[n]==2&&PrimeQ[n+2],AppendTo[A241809,n]],{n,1000}];A241809

%t Select[Prime[Range[200]]-2,PrimeOmega[#]==2&] (* _Harvey P. Dale_, Aug 06 2015 *)

%t SequencePosition[Table[Which[PrimeQ[n],1,PrimeOmega[n]==2,2,True,0],{n,800}],{2,_,1}][[;;,1]] (* _Harvey P. Dale_, Oct 05 2023 *)

%o (PARI) for(k=1, 1000, if(bigomega(k)==2 && isprime(k+2), print1(k, ", "))) \\ _Colin Barker_, May 07 2014

%Y Cf. A001358, A062721, A063638, A107986.

%K nonn,easy

%O 1,1

%A _K. D. Bajpai_, Apr 29 2014

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)