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 1-4 of 4 results.

A121938 Primes of the form (3^k + 5^k)/2^3 = A074606(k)/8.

Original entry on oeis.org

19, 421, 10039, 95383574161, 2384331073699, 1925929944387235853055979210606894889560480247048440342330377620014353281101
Offset: 1

Views

Author

Zak Seidov, Sep 10 2006

Keywords

Comments

Corresponding numbers k such that (3^k + 5^k)/8 is prime are listed in A122853. All these numbers are primes. - Alexander Adamchuk, Sep 14 2006
The next term is too large to include. - Alexander Adamchuk, Sep 14 2006

Crossrefs

Programs

  • Mathematica
    Do[f=5^n+3^n;If[PrimeQ[f/2^3],Print[{n,f/2^3}]],{n,1,1231}] (* Alexander Adamchuk, Sep 14 2006 *)

Formula

a(n) = (A122853(n)^3 + A122853(n)^5)/8. a(n) = A074606[A122853(n)]/8 = A081186[A122853(n)]/4. a(n) = A079773[A122853(n)]. - Alexander Adamchuk, Sep 14 2006

Extensions

More terms from Alexander Adamchuk, Sep 14 2006

A337676 a(0) = 1; a(n) = -(n!)^3 * Sum_{k=0..n-1} a(k) / (k! * (n-k))^3.

Original entry on oeis.org

1, -1, 7, -170, 9664, -1080824, 207876968, -63709383408, 29068641741312, -18924533538121728, 16870738405288439808, -20048074289311310521344, 30889296893650981899202560, -60580966918820974514054369280, 148238116513927185591120536580096
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 15 2020

Keywords

Crossrefs

Programs

  • Mathematica
    a[0] = 1; a[n_] := a[n] = -(n!)^3 Sum[a[k]/(k! (n - k))^3, {k, 0, n - 1}]; Table[a[n], {n, 0, 14}]
    nmax = 14; CoefficientList[Series[1/(1 + PolyLog[3, x]), {x, 0, nmax}], x] Range[0, nmax]!^3
  • PARI
    a(n)={n!^3*polcoef(1/(1 + polylog(3,x + O(x*x^n))), n)} \\ Andrew Howroyd, Sep 15 2020

Formula

Sum_{n>=0} a(n) * x^n / (n!)^3 = 1 / (1 + polylog(3,x)).

A337677 a(0) = 1; a(n) = -(n!)^4 * Sum_{k=0..n-1} a(k) / (k! * (n-k))^4.

Original entry on oeis.org

1, -1, 15, -1150, 277760, -164021776, 200693093392, -455136213439776, 1760342776470958080, -10907982472777142353920, 103006437933467240856354816, -1424284967682216438413265543168, 27890228890526992620507064048877568, -752281114397558490715695708227012591616
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 15 2020

Keywords

Crossrefs

Programs

  • Mathematica
    a[0] = 1; a[n_] := a[n] = -(n!)^4 Sum[a[k]/(k! (n - k))^4, {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]
    nmax = 13; CoefficientList[Series[1/(1 + PolyLog[4, x]), {x, 0, nmax}], x] Range[0, nmax]!^4
  • PARI
    a(n)={n!^4*polcoef(1/(1 + polylog(4,x + O(x*x^n))), n)} \\ Andrew Howroyd, Sep 15 2020

Formula

Sum_{n>=0} a(n) * x^n / (n!)^4 = 1 / (1 + polylog(4,x)).

A337678 a(0) = 1; a(n) = -(n!)^5 * Sum_{k=0..n-1} a(k) / (k! * (n-k))^5.

Original entry on oeis.org

1, -1, 31, -7322, 7281664, -22105862624, 166969429228448, -2726003940127256256, 86768429205346333655040, -4977000682976771751013908480, 483455102073887625685155978412032, -75632981854199587114694850276377296896, 18281294958403743105166278735321854559387648
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 15 2020

Keywords

Crossrefs

Programs

  • Mathematica
    a[0] = 1; a[n_] := a[n] = -(n!)^5 Sum[a[k]/(k! (n - k))^5, {k, 0, n - 1}]; Table[a[n], {n, 0, 12}]
    nmax = 12; CoefficientList[Series[1/(1 + PolyLog[5, x]), {x, 0, nmax}], x] Range[0, nmax]!^5
  • PARI
    a(n)={n!^5*polcoef(1/(1 + polylog(5,x + O(x*x^n))), n)} \\ Andrew Howroyd, Sep 15 2020

Formula

Sum_{n>=0} a(n) * x^n / (n!)^5 = 1 / (1 + polylog(5,x)).
Showing 1-4 of 4 results.