

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



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
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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



