A363270 - OEIS

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A363270

The result, starting from n, of Collatz steps x -> (3x+1)/2 while odd, followed by x -> x/2 while even.

1, 1, 1, 1, 1, 3, 13, 1, 7, 5, 13, 3, 5, 7, 5, 1, 13, 9, 11, 5, 1, 11, 5, 3, 19, 13, 31, 7, 11, 15, 121, 1, 25, 17, 5, 9, 7, 19, 67, 5, 31, 21, 49, 11, 17, 23, 121, 3, 37, 25, 29, 13, 5, 27, 47, 7, 43, 29, 67, 15, 23, 31, 91, 1, 49, 33, 19, 17, 13, 35, 121, 9, 55

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

COMMENTS

Each x -> (3x+1)/2 step decreases the number of trailing 1-bits by 1 so A007814(n+1) of them, and the result of those steps is 2*A085062(n).

LINKS

Dustin Theriault, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = OddPart((3/2)^A007814(n+1)*(n+1) - 1), where OddPart(t) = A000265(t).

a(n) = OddPart(A085062(n)).

MATHEMATICA

OddPart[x_] := x / 2^IntegerExponent[x, 2]