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 A225424 #3 May 22 2013 14:05:31
%S A225424 5,0,3,37,7,17,11,101,61,19,41,197,109,229,31
%N A225424 Least prime p such that prime(n) is the next prime number in the Collatz (3x+1) iteration of p, or 0 if there is no such prime.
%C A225424 The next term, surprisingly, is the 2743-digit (53 * 2^9107 - 1)/3. See A177331 for additional prime numbers, besides 3, that are not in the Collatz iteration of any prime number.
%e A225424 a(4) = 37 because the Collatz iteration of 37 is {37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1}, which shows that 7 is the next prime after 37.
%t A225424 Table[p = Prime[n]; If[p == 3, q = 0, k = 1; While[q = (p*2^k - 1)/3; k < 10000 && ! PrimeQ[q], k++]]; q, {n, 15}]
%Y A225424 Cf. A070165, A177330, A177331.
%K A225424 nonn
%O A225424 1,1
%A A225424 _T. D. Noe_, May 22 2013