A057359 a(n) = floor(5*n/7).

0, 0, 1, 2, 2, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 17, 18, 19, 20, 20, 21, 22, 22, 23, 24, 25, 25, 26, 27, 27, 28, 29, 30, 30, 31, 32, 32, 33, 34, 35, 35, 36, 37, 37, 38, 39, 40, 40, 41, 42, 42, 43, 44, 45, 45, 46, 47, 47, 48, 49, 50, 50, 51

Offset

0,4

Comments

The cyclic pattern (and numerator of the gf) is computed using Euclid's algorithm for GCD.

References

N. Dershowitz and E. M. Reingold, Calendrical Calculations, Cambridge University Press, 1997.

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, NY, 1994.

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

N. Dershowitz and E. M. Reingold, Calendrical Calculations Web Site.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).

Formula

G.f. x^2*(1+x+x^3+x^4+x^5) / ( (x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2 ). Numerator corrected Feb 20 2011

Sum_{n>=2} (-1)^n/a(n) = sqrt(10-2*sqrt(5))*Pi/10 + log(phi)/sqrt(5) - log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Sep 30 2022

Mathematica

Floor[5 Range[0, 75]/7]  (* Harvey P. Dale, Mar 18 2011 *)

Prog

(PARI) a(n)=5*n\7 \\ Charles R Greathouse IV, Sep 02 2015
(Magma) [Floor(5*n/7): n in [0..50]]; // G. C. Greubel, Nov 02 2017

Crossrefs

Floors of other ratios: A004526, A002264, A002265, A004523, A057353, A057354, A057355, A057356, A057357, A057358, A057359, A057360, A057361, A057362, A057363, A057364, A057365, A057366, A057367.

Cf. A001622.

Sequence in context: A274616 A257175 A210357 * A076538 A138466 A247784

Adjacent sequences: A057356 A057357 A057358 * A057360 A057361 A057362

Keyword

nonn,easy

Author

Mitch Harris

Status

approved