

A231610


The least k such that the Collatz (3x+1) iteration of k contains 2^n as the largest power of 2.


1



1, 2, 4, 8, 3, 32, 21, 128, 75, 512, 151, 2048, 1365, 8192, 5461, 32768, 14563, 131072, 87381, 524288, 184111, 2097152, 932067, 8388608, 5592405, 33554432, 13256071, 134217728, 26512143, 536870912, 357913941, 2147483648, 1431655765, 8589934592, 3817748707
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OFFSET

0,2


COMMENTS

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}.


LINKS

Table of n, a(n) for n=0..34.


FORMULA

a(n) = 2^n for odd n.


EXAMPLE

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.


MATHEMATICA

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


CROSSREFS

Cf. A010120, A054646 (similar sequences).
Cf. A135282, A232503 (largest power of 2 in the Collatz iteration of n).
Cf. A225124.
Sequence in context: A243065 A289271 A223699 * A225124 A059884 A191561
Adjacent sequences: A231607 A231608 A231609 * A231611 A231612 A231613


KEYWORD

nonn


AUTHOR

T. D. Noe, Dec 02 2013


STATUS

approved



