%I #24 Sep 08 2022 08:45:17

%S 14,34,142,898,1762,5182,19042,79522,213442,359998,412162,627238,

%T 685582,777922,1192462,1299478,1695202,2005006,2585662,2663398,

%U 3849322,4536898,5143822,5588446,5673922,6594502,7225342,8363638,8538058,12110278

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

%C 5 is the only odd number of the form prime(n)*prime(n+1) - 1. - _Klaus Brockhaus_, Mar 29 2005

%C 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 Ray Chandler, <a href="/A103533/b103533.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1)=14 because prime(2)*prime(3)- 1=3*5-1=14=2*7;

%e a(2)=34 because prime(3)*prime(4)- 1=5*7-1=34=2*17;

%e a(3)=142 because prime(5)*prime(6)-1=11*13-1=142=2*71.

%t 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 Select[Times@@#-1&/@Partition[Prime[Range[500]],2,1],EvenQ[#] && PrimeOmega[ #]==2&] (* _Harvey P. Dale_, Apr 24 2018 *)

%o (PARI) for(n=1,490,if(bigomega(k=prime(n)*prime(n+1)-1)==2,print1(k,","))) \\ _Klaus Brockhaus_, Mar 24 2005

%o (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 Cf. A001358, A006881, A086870, A103746, A269663.

%K easy,nonn

%O 1,1

%A _Giovanni Teofilatto_, Mar 22 2005

%E More terms from _Robert G. Wilson v_ and _Klaus Brockhaus_, Mar 24 2005