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A222294 Least k such that a term of the Collatz (3x+1) iteration of k is divisible by prime(n). 1

%I #5 Feb 22 2013 17:33:09

%S 2,3,3,7,7,7,7,19,15,19,27,37,27,43,27,15,39,27,39,27,73,27,27,27,63,

%T 39,27,27,109,75,127,87,27,123,99,151,123,163,27,115,79,27,127,171,87,

%U 199,187,223,151,135,27,159,241,27,171,27,79,271,277,187,27,27,307

%N Least k such that a term of the Collatz (3x+1) iteration of k is divisible by prime(n).

%C Note that a(n) <= prime(n). The following primes require the maximum number of iterations: 2, 3, 7, 19, 37, 43, 73, 109, 127,...

%H T. D. Noe, <a href="/A222294/b222294.txt">Table of n, a(n) for n = 1..1000</a>

%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[p = Prime[n]; k = 1; While[Select[Collatz[k], Mod[#, p] == 0 &] == {}, k++]; k, {n, 100}]

%Y Cf. A070165.

%K nonn

%O 1,1

%A _T. D. Noe_, Feb 22 2013

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