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

Author

Mitch Harris

Keywords

• nonn
• easy

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).

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.

Programs

Magma

[Floor(5*n/7): n in [0..50]]; // G. C. Greubel, Nov 02 2017

Mathematica

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

PARI

a(n)=5*n\7 \\ Charles R Greathouse IV, Sep 02 2015

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