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%I #15 Sep 22 2015 05:09:24
%S 2,7,17,29,31,71,89,107,113,127,131,157,181,223,239,263,271,277,281,
%T 283,313,337,379,409,419,421,431,503,547,571,577,691,701,727,757,809,
%U 821,857,883,947,953,971,1031,1109,1129,1153,1163,1231,1283,1291,1327,1361,1447,1487,1531,1559,1567,1583
%N Primes p such that A008908(p) is also prime.
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e 7 is prime and A008908(7) is 17, which is also prime. Therefore, 7 is in the sequence.
%t collatz[n_]:=If[EvenQ[n],n/2,3*n+1];
%t seq[n_]:=Length[NestWhileList[collatz,n,#!= 1&]]
%t Select[Flatten[Position[seq/@Range[7!],_?PrimeQ]],PrimeQ]
%o (PARI) T(n)=c=0;while(n!=1,if(n%2,n=3*n+1;c++);if(!(n%2),n=n/2;c++));c+1
%o forprime(p=1,10^3,if(isprime(T(p)),print1(p,", "))) \\ _Derek Orr_, Aug 27 2015
%Y Cf. A008908.
%K easy,nonn
%O 1,1
%A _Ivan N. Ianakiev_, Jul 31 2015