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%I #7 Dec 09 2013 13:47:15
%S 1,2,4,8,3,32,21,128,75,512,151,2048,1365,8192,5461,32768,14563,
%T 131072,87381,524288,184111,2097152,932067,8388608,5592405,33554432,
%U 13256071,134217728,26512143,536870912,357913941,2147483648,1431655765,8589934592,3817748707
%N The least k such that the Collatz (3x+1) iteration of k contains 2^n as the largest power of 2.
%C Very similar to A225124, where 2^n is the largest number in the Collatz iteration of A225124(n). The only difference appears to be a(8), which is 75 here and 85 in A225124. The Collatz iteration of 75 is {75, 226, 113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1}.
%F a(n) = 2^n for odd n.
%e The iteration for 21 is {21, 64, 32, 16, 8, 4, 2, 1}, which shows that 64 = 2^6 is a term. However, 32 is not the first power of two. We have to wait until the iteration for 32, which is {32, 16, 8, 4, 2, 1}, to see 32 = 2^5 as the first power of two.
%t Collatz[n_?OddQ] := 3*n + 1; Collatz[n_?EvenQ] := n/2; nn = 21; t = Table[-1, {nn}]; n = 0; cnt = 0; While[cnt < nn, n++; q = Log[2, NestWhile[Collatz, n, Not[IntegerQ[Log[2, #]]] &]]; If[q < nn && t[[q + 1]] == -1, t[[q + 1]] = n; cnt++]]; t
%Y Cf. A010120, A054646 (similar sequences).
%Y Cf. A135282, A232503 (largest power of 2 in the Collatz iteration of n).
%Y Cf. A225124.
%K nonn
%O 0,2
%A _T. D. Noe_, Dec 02 2013
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