A164291 - OEIS

%I #6 Sep 24 2013 00:41:43

%S 3,11,59,71,239,191,2111,1151,14591,26111,15359,139967,138239,675839,

%T 2101247,737279,4866047,786431,22118399,36175871,194641919,63700991,

%U 138412031,169869311,1321205759,11123294207,16357785599,4076863487,25165823999,10871635967

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

%C 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).

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

%H Donovan Johnson, <a href="/A164291/b164291.txt">Table of n, a(n) for n = 2..200</a>

%e 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.

%e The sequence oscillates and here we see that a(7)<a(6)=239.

%t 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]

%Y Cf. A060213, A102168, A164289, A164290.

%K nonn

%O 2,1

%A _Carlos Alves_, Aug 12 2009

%E Definition and comments corrected, a(2) and a(20)-a(29) from _Donovan Johnson_, Aug 20 2009