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.

Showing 1-3 of 3 results.

A262786 a(n) = 37^(2*n+1).

Original entry on oeis.org

37, 50653, 69343957, 94931877133, 129961739795077, 177917621779460413, 243569224216081305397, 333446267951815307088493, 456487940826035155404146917, 624931990990842127748277129373, 855531895666462872887391390111637, 1171223165167387672982838813062831053
Offset: 0

Views

Author

Vincenzo Librandi, Oct 08 2015

Keywords

Comments

37*a(n) is a square.

Crossrefs

Second bisection of A009981 (powers of 37).
Cf. similar sequences listed in A262715.

Programs

  • Magma
    [37^(2*n+1): n in [0..15]];
    
  • Mathematica
    37^Range[1, 30, 2]
  • PARI
    vector(20, n, n--; 37^(2*n+1)) \\ Altug Alkan, Oct 08 2015

Formula

G.f.: 37/(1 - 1369*x).
a(n) = 1369*a(n-1).
a(n) = A009981(A005408(n)). - Wesley Ivan Hurt, Sep 04 2022

A262716 a(n) = 31^(2*n+1).

Original entry on oeis.org

31, 29791, 28629151, 27512614111, 26439622160671, 25408476896404831, 24417546297445042591, 23465261991844685929951, 22550116774162743178682911, 21670662219970396194714277471, 20825506393391550743120420649631, 20013311644049280264138724244295391
Offset: 0

Views

Author

Vincenzo Librandi, Oct 07 2015

Keywords

Comments

31*a(n) is a square.
In general, Sum_{i>=0} 1/m^(2*i+1) = m/(m^2-1) when |m|>1. In this case, Sum_{i>=0} 1/a(i) = 31/960. [Bruno Berselli, Oct 07 2015]

Crossrefs

Second bisection of A009975 (powers of 31).
Cf. similar sequences listed in A262715.

Programs

  • Magma
    [31^(2*n+1): n in [0..15]];
    
  • Mathematica
    31^Range[1, 30, 2]
  • PARI
    Vec(31/(1 - 961*x) + O(x^30)) \\ Michel Marcus, Oct 07 2015
    
  • PARI
    vector(15, n, n--; 31^(2*n+1)) \\ Bruno Berselli, Oct 07 2015
    
  • Sage
    [31^(2*n+1) for n in (0..15)] # Bruno Berselli, Oct 07 2015

Formula

G.f.: 31/(1 - 961*x).
a(n) = 961*a(n-1).

A262787 a(n) = 41^(2*n+1).

Original entry on oeis.org

41, 68921, 115856201, 194754273881, 327381934393961, 550329031716248441, 925103102315013629321, 1555098314991537910888601, 2614120267500775228203738281, 4394336169668803158610484050361, 7386879101213258109624223688656841, 12417343769139486882278320020632149721
Offset: 0

Views

Author

Vincenzo Librandi, Oct 08 2015

Keywords

Comments

41*a(n) is a square.

Crossrefs

Second bisection of A009985 (powers of 41).
Cf. similar sequences listed in A262715.

Programs

  • Magma
    [41^(2*n+1): n in [0..15]];
    
  • Maple
    A262787:=n->41^(2*n+1): seq(A262787(n), n=0..20); # Wesley Ivan Hurt, Dec 26 2016
  • Mathematica
    41^Range[1, 30, 2]
    NestList[1681#&,41,20] (* Harvey P. Dale, Mar 18 2025 *)
  • PARI
    vector(20, n, n--; 41^(2*n+1)) \\ Altug Alkan, Oct 08 2015

Formula

G.f.: 41/(1 - 1681*x).
a(n) = 1681*a(n-1).
Showing 1-3 of 3 results.