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%I #10 Jul 09 2018 23:20:34
%S 1,5,7,12,14,16,29,51,56,58,60,64,65,67,74,75,78,83,87,90,100,102,104,
%T 106,109,115,118,119,122,128,130,132,134,141,142,147,161,166,173,176,
%U 187,188,200,212,219,221,231,234,239,241,251,259,264,293,313,314,316
%N Numbers for which the smallest number of steps to reach 1 in "3x+1" (or Collatz) problem is a prime.
%C Positions of primes in A033491. [_R. J. Mathar_, Nov 01 2010]
%D R. K. Guy, "Collatz's Sequence" in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 215-218, 1994
%D Clifford A. Pickover, Wonders of Numbers, Oxford University Press, pp. 116-118, 2001
%H J. C. Lagarias, <a href="https://www.maa.org/programs/maa-awards/writing-awards/the-3x-1-problem-and-its-generalizations">The 3x+1 Problem and its Generalizations</a>, Amer. Math. Monthly 92, 3-23, 1985
%e 1st Collatz sequence with a(1)=1 step starts with 2=prime(1): 2-1;
%e 1st Collatz sequence with a(3)=7 steps starts with 3=prime(2): 3-10-5-16-8-4-2-1;
%e prime(6)=13 has Collatz sequence with 9 steps: 13-40-20-10-5-16-8-4-2-1, so has the smaller composite 12 < 13: 12-6-3-10-5-16-8-4-2-1 => 9 not a term of sequence;
%e 1st Collatz sequence with a(5)=14 steps starts with 11=prime(5): 11-34-17-52-26-13-40-20-10-5-16-8-4-2-1.
%Y Cf. A070905, A033491, A088975, A126727, A060565
%K nonn
%O 1,2
%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), Dec 10 2009
%E Terms > 187 from _R. J. Mathar_, Nov 01 2010
%E Name edited by _Michel Marcus_, Jul 07 2018
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