A231610 - OEIS

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A231610

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

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: A341811 A332306 A223699 * A225124 A344537 A349104

Adjacent sequences: A231607 A231608 A231609 * A231611 A231612 A231613

KEYWORD

nonn

AUTHOR

T. D. Noe, Dec 02 2013

STATUS

approved