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A103533 Even semiprimes of the form prime(n)*prime(n+1) - 1.

%I A103533 #24 Sep 08 2022 08:45:17
%S A103533 14,34,142,898,1762,5182,19042,79522,213442,359998,412162,627238,
%T A103533 685582,777922,1192462,1299478,1695202,2005006,2585662,2663398,
%U A103533 3849322,4536898,5143822,5588446,5673922,6594502,7225342,8363638,8538058,12110278
%N A103533 Even semiprimes of the form prime(n)*prime(n+1) - 1.
%C A103533 5 is the only odd number of the form prime(n)*prime(n+1) - 1. - _Klaus Brockhaus_, Mar 29 2005
%C A103533 2*A086870(n) is a subsequence of this sequence. They first differ when 313619 is not in A086870, but 2*313619 = 627238 = a(12). This is because 787 and 797 are the first such pair of consecutive primes that are not twins and (787*797-1)/2 is prime. - _Jason Kimberley_, Oct 22 2015
%H A103533 Ray Chandler, <a href="/A103533/b103533.txt">Table of n, a(n) for n = 1..10000</a>
%e A103533 a(1)=14 because prime(2)*prime(3)- 1=3*5-1=14=2*7;
%e A103533 a(2)=34 because prime(3)*prime(4)- 1=5*7-1=34=2*17;
%e A103533 a(3)=142 because prime(5)*prime(6)-1=11*13-1=142=2*71.
%t A103533 fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; Select[ Prime[ Range[490]]*Prime[ Range[2, 491]] - 1, fQ[ # ] &] (* _Robert G. Wilson v_, Mar 24 2005 *)
%t A103533 Select[Times@@#-1&/@Partition[Prime[Range[500]],2,1],EvenQ[#] && PrimeOmega[ #]==2&] (* _Harvey P. Dale_, Apr 24 2018 *)
%o A103533 (PARI) for(n=1,490,if(bigomega(k=prime(n)*prime(n+1)-1)==2,print1(k,","))) \\ _Klaus Brockhaus_, Mar 24 2005
%o A103533 (Magma) [a:n in[2..1000]|IsPrime(a div 2)where a is NthPrime(n)*NthPrime(n+1)-1]; // _Jason Kimberley_, Oct 22 2015
%Y A103533 Cf. A001358, A006881, A086870, A103746, A269663.
%K A103533 easy,nonn
%O A103533 1,1
%A A103533 _Giovanni Teofilatto_, Mar 22 2005
%E A103533 More terms from _Robert G. Wilson v_ and _Klaus Brockhaus_, Mar 24 2005