cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-14 of 14 results.

A057362 a(n) = floor(5*n/13).

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 28, 28, 29
Offset: 0

Views

Author

Mitch Harris

Keywords

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

Crossrefs

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

Programs

  • Magma
    [Floor(5*n/13): n in [0..50]]; // G. C. Greubel, Nov 02 2017
  • Mathematica
    Table[Floor[5*n/13], {n, 0, 50}] (* G. C. Greubel, Nov 02 2017 *)
LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,0,0,1,-1},{0,0,0,1,1,1,2,2,3,3,3,4,4,5},80] (* Harvey P. Dale, Dec 12 2021 *)
  • PARI
    a(n)=5*n\13 \\ Charles R Greathouse IV, Sep 02 2015

Formula

G.f.: x^3*(1 + x^3 + x^5 + x^8 + x^10) / ( (x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x-1)^2 ). [Numerator corrected Feb 20 2011]
Sum_{n>=3} (-1)^(n+1)/a(n) = sqrt(1-2/sqrt(5))*Pi/5 + arccosh(7/2)/(2*sqrt(5)) + log(2)/5. - Amiram Eldar, Sep 30 2022

A057363 a(n) = floor(8*n/13).

Original entry on oeis.org

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

Views

Author

Mitch Harris

Keywords

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

Crossrefs

Floors of other ratios: A004526, A002264, A002265, A004523, A057353, A057354, A057355, A057356, A057357, A057358, A057359, A057360, A057361, A057362, A057363, A057364, A057365, A057366, A057367.
Note that 20 appears twice. Different from A005206, A060143.

Programs

  • Magma
    [Floor(8*n/13): n in [0..50]]' // G. C. Greubel, Nov 02 2017
  • Mathematica
    Table[Floor[8*n/13], {n, 0, 50}] (* G. C. Greubel, Nov 02 2017 *)
LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,0,0,1,-1},{0,0,1,1,2,3,3,4,4,5,6,6,7,8},80] (* Harvey P. Dale, Jul 21 2020 *)
  • PARI
    a(n)=8*n\13 \\ Charles R Greathouse IV, Sep 02 2015

Formula

a(n) = a(n-1) + a(n-13) - a(n-14).
G.f.: x^2*(1+x)*(x^2 - x + 1)*(x^8 + x^7 + x^2 + 1)/( (x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x-1)^2 ). [Numerator corrected Feb 20 2011]

A057364 a(n) = floor(8*n/21).

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 28, 28, 28, 29
Offset: 0

Views

Author

Mitch Harris

Keywords

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

Crossrefs

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

Programs

Formula

a(n) = a(n-1) + a(n-21) - a(n-22).
G.f.: x^3*(1+x)*(x^4 - x^3 + x^2 - x + 1)*(x^13 + x^11 + x^3 + 1) / ( (1 + x + x^2)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1)*(x-1)^2 ). [Numerator corrected by R. J. Mathar, Feb 20 2011]

A057366 a(n) = floor(7*n/19).

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 28
Offset: 0

Views

Author

Mitch Harris

Keywords

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

Crossrefs

Similar pattern in Hebrew leap years A057349. Floors of other ratios: A004526, A002264, A002265, A004523, A057353, A057354, A057355, A057356, A057357, A057358, A057359, A057360, A057361, A057362, A057363, A057364, A057365, A057366, A057367.

Programs

Formula

a(n) = a(n-1) + a(n-19) - a(n-20).
G.f.: x^3*(x^2-x+1)*(x^14 + x^13 + x^12 - x^10 + x^8 + x^7 + x^6 + x + 1)/( (x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x-1)^2 ). [Corrected by R. J. Mathar, Feb 20 2011]
Previous Showing 11-14 of 14 results.

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