A263574 Beatty sequence for 1/sqrt(3) - log(phi)/3575 where phi is the golden ratio, A001622.

0, 0, 1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 21, 22, 23, 23, 24, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 32, 33, 34, 34, 35, 35, 36, 36, 37, 38, 38, 39, 39, 40, 40, 41, 42, 42, 43

Offset

0,5

Comments

The number 1/sqrt(3) - log(phi)/3575 (=0.577215664483...) is an approximation to Euler's constant (A001620) (=0.577215664901...).

M. Hudson found a similar Euler-Mascheroni constant approximation (see link), 1/sqrt(3)-1/7429 (=0.57721566157...).

Links

Karl V. Keller, Jr., Table of n, a(n) for n = 0..100000

Xavier Gourdon and Pascal Sebah, Collection of formulas for Euler's constant,Euler's constant.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant.

Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant Approximations.

Formula

a(n) = floor(n*(1/sqrt(3) - log(phi)/3575)).

a(n) = A038128(n) for n < 58628.

Example

For n=9, floor(9*(0.577215664483)) = floor(5.194940980347) = 5.

Mathematica

Table[Floor[n (1/Sqrt@ 3 - Log[GoldenRatio]/3575)], {n, 0, 75}] (* Michael De Vlieger, Nov 12 2015 *)

Prog

(Python)
from sympy import floor, log, sqrt
for n in range(0, 101):print(floor(n*(1/sqrt(3)-log(1/2+sqrt(5)/2)/3575)), end=', ')
(PARI) {phi = (1+sqrt(5))/2}; vector(100, n, n--; floor(n*(1/sqrt(3) - log(phi)/3575))) \\ G. C. Greubel, Sep 05 2018
(Magma) phi:= (1+Sqrt(5))/2; [Floor(n*(1/Sqrt(3) - Log(phi)/3575)): n in [0..100]]; // G. C. Greubel, Sep 05 2018

Crossrefs

Cf. A001620, A020760 (1/sqrt(3)), A038128 (Beatty sequence for Euler's constant), A097337 (Beatty sequence for 1/sqrt(3)).

Sequence in context: A057358 A038128 A097337 * A366701 A278496 A353283

Adjacent sequences: A263571 A263572 A263573 * A263575 A263576 A263577

Keyword

nonn,changed

Author

Karl V. Keller, Jr., Oct 21 2015

Status

approved