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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
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
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.
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved