A224996 - OEIS

A224996

Floor(1/f(x^(1/n))) for x = 2, where f computes the fractional part.

2, 3, 5, 6, 8, 9, 11, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 39, 41, 42, 44, 45, 47, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 88, 90, 91, 93, 94, 96, 97

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OFFSET

2,1

COMMENTS

First denominator of continued fraction representing 2^(1/n): [1,a(n),....] so that 1+1/a(n) is first convergent for 2^(1/n). - Carmine Suriano, Apr 29 2014

LINKS

Table of n, a(n) for n=2..68.

Melvyn B. Nathanson, On the fractional parts of roots of positive real numbers, Amer. Math. Monthly, 120 (2013), 409-429.

FORMULA

a(n) = floor(n/log(2)-1/2). - Andrey Zabolotskiy, Dec 01 2017

MATHEMATICA

th = 2; t = Table[Floor[1/FractionalPart[th^(1/n)]], {n, 2, 100}]

CROSSREFS

Cf. A224995, A224997, A224998, A001651, A047211, A047203, A047290, A047332.

Sequence in context: A184624 A093001 A226721 * A373112 A246046 A026428

Adjacent sequences: A224993 A224994 A224995 * A224997 A224998 A224999

KEYWORD

nonn,easy

AUTHOR

T. D. Noe, Apr 26 2013

STATUS

approved