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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A155979 Decimal expansion of log_10 (24).

Original entry on oeis.org

1, 3, 8, 0, 2, 1, 1, 2, 4, 1, 7, 1, 1, 6, 0, 6, 0, 2, 2, 9, 3, 6, 2, 4, 4, 5, 8, 7, 4, 2, 8, 5, 9, 4, 3, 8, 9, 5, 0, 4, 6, 9, 8, 5, 0, 8, 5, 7, 7, 0, 2, 1, 4, 8, 8, 7, 6, 1, 1, 4, 8, 0, 2, 3, 6, 8, 6, 5, 5, 3, 7, 2, 0, 6, 0, 6, 9, 3, 4, 6, 5, 1, 5, 0, 3, 7, 5, 0, 1, 1, 2, 0, 0, 2, 1, 7, 4, 8, 1
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2009

Keywords

Examples

			1.3802112417116060229362445874285943895046985085770214887611...

Links

Crossrefs

Cf. decimal expansion of log_10(m): A007524 (m=2), A114490 (m=3), A114493 (m=4), A153268 (m=5), A153496 (m=6), A153620 (m=7), A153790 (m=8), A104139 (m=9), A154182 (m=11), A154203 (m=12), A154368 (m=13), A154478 (m=14), A154580 (m=15), A154794 (m=16), A154860 (m=17), A154953 (m=18), A155062 (m=19), A155522 (m=20), A155677 (m=21), A155746 (m=22), A155830 (m=23).

Programs

A007957 Numbers that contain an odd digit.

Original entry on oeis.org

1, 3, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 25, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43, 45, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 63, 65, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 83, 85, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100
Offset: 1

Views

Author

R. Muller

Keywords

Comments

Complement of A014263; A196564(a(n)) > 0; A103181(a(n)) > 0. - Reinhard Zumkeller, Oct 04 2011

Links

Crossrefs

Cf. A014263, A103181, A196564.

Programs

  • Haskell
    import Data.List (findIndices)
a007957 n = a007957_list !! (n-1)
a007957_list = findIndices (> 0) a196564_list
a196564 n = length [d | d <- show n, d `elem` "13579"]
a196564_list = map a196564 [0..]
-- Reinhard Zumkeller, Oct 04 2011
  • Mathematica
    Select[Range[100],Count[IntegerDigits[#],?OddQ]>0&] (* _Harvey P. Dale, Sep 06 2017 *)
  • PARI
    is(n)=my(v=vecsort(eval(Vec(Str(n)))%2,,8));v[#v] \\ Charles R Greathouse IV, Jul 25 2012

Formula

a(n) = n + O(n^0.69897...) where the constant is A153268. - Charles R Greathouse IV, Jul 25 2012

A153265 a(n) = (-2*I)^n + (2*I)^n + (1/2 + 1/2*I*sqrt(3))^n + (1/2 - 1/2*I*sqrt(3))^n.

Original entry on oeis.org

4, 1, -9, -2, 31, 1, -126, 1, 511, -2, -2049, 1, 8194, 1, -32769, -2, 131071, 1, -524286, 1, 2097151, -2, -8388609, 1, 33554434, 1, -134217729, -2, 536870911, 1, -2147483646, 1, 8589934591, -2, -34359738369, 1
Offset: 0

Views

Author

Creighton Dement, Dec 22 2008, Dec 31 2008

Keywords

Comments

For all n there is an m such that: ||a(n)| - 2^m| <= 2. In the Python program which will be provided, the sequence (a(n)) is given by 4tesseq(X) where X = 1.5'i + .25(ii + jj + kk + ee) is the generating floretion.

Examples

			a(4) = 32 + (1/2 + 1/2*I*sqrt(3))^4 + (1/2 - 1/2*I*sqrt(3))^4 = 31 -or- a(4) = a(n-1) - 5a(n-2) + 4a(n-3) - 4a(n-4) = -2 - 5*(-9) + 4*(1) - 4*4 = 31

Links

Crossrefs

Cf. A153266, A153267, A153268.

Programs

  • Magma
    I:=[4,1,-9,-2]; [n le 4 select I[n] else Self(n-1)-5*Self(n-2)+4*Self(n-3) -4*Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 26 2014
  • Maple
    a := n-> (2*I)^n+(-2*I)^n+(1/2+1/2*I*sqrt(3))^n+(1/2-1/2*I*sqrt(3))^n;
  • Mathematica
    CoefficientList[Series[4 + x (1 - 10 x + 12 x^2 - 16 x^3)/((x^2 - x + 1) (4 x^2 + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 26 2014 *)
  • PARI
    a(n)=2*(n%2<1)*(-4)^(n\2)+3*(n%3<1)*(-1)^(n\3)-(-1)^n \\ Tani Akinari, Jun 25 2014

Formula

a(n) = a(n-1) - 5a(n-2) + 4a(n-3) - 4a(n-4).
G.f.: 4 + x*(1-10*x+12*x^2-16*x^3)/((x^2-x+1)*(4*x^2+1)). - corrected by Vaclav Kotesovec, Jun 25 2014
Previous Showing 21-23 of 23 results.

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

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