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

2,1

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).

Links

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

Example

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.

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]

Crossrefs

Cf. A060213, A102168, A164289, A164290.

Sequence in context: A089188 A086827 A308487 * A137690 A107007 A199854

Adjacent sequences: A164288 A164289 A164290 * A164292 A164293 A164294

Keyword

nonn

Author

Carlos Alves, Aug 12 2009

Extensions

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

Status

approved