A164291 a(n) = p is the first twin prime (p, p+2) for which p+1 has n prime factors (n>=2, multiplicity counted).

3, 11, 59, 71, 239, 191, 2111, 1151, 14591, 26111, 15359, 139967, 138239, 675839, 2101247, 737279, 4866047, 786431, 22118399, 36175871, 194641919, 63700991, 138412031, 169869311, 1321205759, 11123294207, 16357785599, 4076863487, 25165823999, 10871635967

Offset: 2

Author

Carlos Alves, Aug 12 2009

Keywords

• nonn

Comments

a(3)-a(6) are the first elements of A060213, A102168, A164289, A164290 respectively with n=3,4,5,6 (prime factors in the middle number).

This gives the first p with (p,p+2) twin primes and Omega(p+1)=n with n>=2 (n=1 is impossible).

Examples

			a(7)=191 because in (191, 192, 193) we have Omega(192)=Omega(2*2*2*2*2*2*3)=7 and 191, 193 are twin primes.
The sequence oscillates and here we see that a(7)<a(6)=239.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 2..200

Crossrefs

Cf. A060213, A102168, A164289, A164290.

Programs

Mathematica

Omega = If[ # == 1, 0, Apply[Plus, Transpose[FactorInteger[ # ]][[2]]]] &; Wmil = Map[Omega, Range[1, 10000000]]; Aseq=(Flatten@Position[Partition[Wmil, 3, 1], {1, #, 1}])[[1]] & /@ Range[3,19]

Extensions

Definition and comments corrected, a(2) and a(20)-a(29) from Donovan Johnson, Aug 20 2009