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A057355 a(n) = floor(3*n/5). 17
0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 33, 33, 34, 34, 35, 36, 36, 37, 37, 38, 39, 39, 40, 40, 41, 42, 42, 43, 43 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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

The sequence can be obtained from A008588 by deleting the last digit of each term. - Bruno Berselli, Sep 11 2019

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 (1,0,0,0,1,-1).

FORMULA

G.f.: x^2*(1 + x^2 + x^3)/((1 - x)*(1 - x^5)). - Bruce Corrigan (scentman(AT)myfamily.com), Jul 03 2002

For all m>=0: a(5m)=0 mod 3; a(5m+1)=0 mod 3; a(5m+2)=1 mod 3; a(5m+3)=1 mod 3; a(5m+4)=2 mod 3.

a(n) = -1 + Sum_{k=0..n} (1/50)*(3*(k mod 5) - 7*((k+1) mod 5) + 13*((k+2) mod 5) - 7*((k+3) mod 5) + 13*((k+4) mod 5)). - Paolo P. Lava, Nov 17 2008

Sum_{n>=2} (-1)^n/a(n) = Pi/(3*sqrt(3)) - log(2)/3. - Amiram Eldar, Sep 30 2022

MATHEMATICA

Table[Floor[3*n/5], {n, 0, 50}] (* G. C. Greubel, Nov 02 2017 *)

PROG

(PARI) a(n)=3*n\5 \\ Charles R Greathouse IV, Sep 02 2015

(Magma) [3*n div 5: n in [0..80]]; // Bruno Berselli, Dec 07 2016

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. A008588.

Sequence in context: A139338 A244229 A317596 * A171975 A160511 A079952

Adjacent sequences:  A057352 A057353 A057354 * A057356 A057357 A057358

KEYWORD

nonn,easy,changed

AUTHOR

Mitch Harris

STATUS

approved

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Last modified September 30 20:49 EDT 2022. Contains 357106 sequences. (Running on oeis4.)