This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A177330 #2 Mar 30 2012 17:22:56
%S A177330 3,0,1,4,1,2,1,4,3,1,2,4,3,4,1,9107,3,6,2,1,2,4,7,1,6,1,2,1,32,11,4,3,
%T A177330 45,24,3,6,8,16,21,3,29,2,1,2,1,4,2,66,1,8,7,5,10,1,5,3,1,14,18,13,6,
%U A177330 59,2,3,4,1,18,2,5,4,3,1,6,5016,8,3,15,14,3,12,3,46,5,2,4,3,5,4,1,2,1,3
%N A177330 Least k>0 such that (p*2^k-1)/3 is prime, or zero if no k exists, where p=prime(n).
%C A177330 When a(n) is not zero, a(n) is even if p=1 (mod 6); a(n) is odd if p=5 (mod 6). If we let q=(p*2^k-1)/3 be a prime generated by p for some k>0, then the first prime number after q in the Collatz iteration of q is p. When k=1, q is less than p. The primes, other than 3, for which a(n)=0 are in A177331.
%t A177330 Table[p=Prime[n]; If[p==3, k=0, k=1; While[q=(p*2^k-1)/3; k<10000 && !PrimeQ[q], k++ ]]; k, {n,100}]
%Y A177330 Cf. A177000
%K A177330 nonn
%O A177330 1,1
%A A177330 _T. D. Noe_, May 08 2010