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

14, 34, 142, 898, 1762, 5182, 19042, 79522, 213442, 359998, 412162, 627238, 685582, 777922, 1192462, 1299478, 1695202, 2005006, 2585662, 2663398, 3849322, 4536898, 5143822, 5588446, 5673922, 6594502, 7225342, 8363638, 8538058, 12110278

Offset: 1

Author

Giovanni Teofilatto, Mar 22 2005

Keywords

• easy
• nonn

Comments

5 is the only odd number of the form prime(n)*prime(n+1) - 1. - Klaus Brockhaus, Mar 29 2005

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

Examples

			a(1)=14 because prime(2)*prime(3)- 1=3*5-1=14=2*7;
a(2)=34 because prime(3)*prime(4)- 1=5*7-1=34=2*17;
a(3)=142 because prime(5)*prime(6)-1=11*13-1=142=2*71.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A006881, A086870, A103746, A269663.

Programs

Magma

[a:n in[2..1000]|IsPrime(a div 2)where a is NthPrime(n)*NthPrime(n+1)-1]; // Jason Kimberley, Oct 22 2015

Mathematica

fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; Select[ Prime[ Range[490]]*Prime[ Range[2, 491]] - 1, fQ[ # ] &] (* Robert G. Wilson v, Mar 24 2005 *)
Select[Times@@#-1&/@Partition[Prime[Range[500]],2,1],EvenQ[#] && PrimeOmega[ #]==2&] (* Harvey P. Dale, Apr 24 2018 *)

PARI

for(n=1,490,if(bigomega(k=prime(n)*prime(n+1)-1)==2,print1(k,","))) \\ Klaus Brockhaus, Mar 24 2005

Extensions

More terms from Robert G. Wilson v and Klaus Brockhaus, Mar 24 2005