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.

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A137936 a(n) = 5*mod(n,5) + floor(n/5).

Original entry on oeis.org

0, 5, 10, 15, 20, 1, 6, 11, 16, 21, 2, 7, 12, 17, 22, 3, 8, 13, 18, 23, 4, 9, 14, 19, 24, 5, 10, 15, 20, 25, 6, 11, 16, 21, 26, 7, 12, 17, 22, 27, 8, 13, 18, 23, 28, 9, 14, 19, 24, 29, 10, 15, 20, 25, 30, 11, 16, 21, 26, 31, 12, 17, 22, 27, 32, 13, 18, 23, 28, 33, 14, 19, 24, 29, 34
Offset: 0

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Author

William A. Tedeschi, Mar 06 2008

Keywords

Examples

			a(0) = 5*mod(0,5) + floor(0/5) = 0
a(3) = 5*mod(3,5) + floor(3/5) = 15

Crossrefs

Cf. A010874, A002266.

Programs

  • Python
    a = lambda n: 5*(n%5) + floor(n/5)

Formula

a(n) = 5*mod(n,5) + floor(n/5) = 5*A010874(n) + A002266(n)
O.g.f.: -x(-5x^3+19x^4-5x^2-5x-5)/[(-1+x)^2*(x^3+x^4+x^2+x+1)] . - R. J. Mathar, Mar 07 2008

A327440 a(n) = floor(3*n/10).

Original entry on oeis.org

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

Views

Author

Bruno Berselli, Sep 11 2019

Keywords

Comments

The sequence can be obtained from A008585 by deleting the last digit of each term.

Links

Crossrefs

Cf. A008585.
Similar sequences with the formula floor(k*n/10): A059995 (k=1); A002266 (k=2); A057354 (k=4); A004526 (k=5); A057355 (k=6); A188511 (k=7); A090223 (k=8).

Programs

  • Julia
    [div(3*n, 10) for n in 0:80] |> println
  • Mathematica
    Table[Floor[3 n/10], {n, 0, 80}]
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3}, 80]
  • PARI
    vector(80, n, n--; floor(3*n/10))

Formula

O.g.f.: x^4*(1 + x^3 + x^6)/((1 + x)*(1 - x)^2*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)) = (x^4 + x^7 + x^10)/(1 - x - x^10 + x^11).
a(n) = a(n-1) + a(n-10) - a(n-11) for n > 10.

A358012 Minimal number of coins needed to pay n cents using coins of denominations 1 and 5 cents.

Original entry on oeis.org

0, 1, 2, 3, 4, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 7, 8, 9, 10, 11, 8, 9, 10, 11, 12, 9, 10, 11, 12, 13, 10, 11, 12, 13, 14, 11, 12, 13, 14, 15, 12, 13, 14, 15, 16, 13, 14, 15, 16, 17, 14, 15, 16, 17, 18, 15, 16
Offset: 0

Views

Author

Sandra Snan, Oct 24 2022

Keywords

Comments

Sequence consists of runs of five consecutive integers: 0..4, 1..5, 2..6, 3..7, etc.

Links

Crossrefs

Cf. A002266, A010874.
Cf. A076314 (1,10 cents), A053344 (1,5,10,25 cents).

Programs

Formula

Sum of quotient and remainder of n/5.
a(n) = A002266(n) + A010874(n).
Previous Showing 51-53 of 53 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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