A224997 Floor(1/f(x^(1/n))) for x = 17, where f computes the fractional part.

8, 1, 32, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25

Offset: 2

Author

T. D. Noe, Apr 26 2013

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A224995, A224996, A224998, A001651, A047211, A047203, A047290, A047332.

Programs

Mathematica

th = 17; t = Table[Floor[1/FractionalPart[th^(1/n)]], {n, 2, 100}]

Formula

a(n) = floor(n/log(17)-1/2) for n>7. - Andrey Zabolotskiy, Dec 01 2017