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.

A061463 Numerator of 1 + 1/(2^2) + 1/(3^3) + ... 1/(n^n).

Original entry on oeis.org

0, 1, 5, 139, 8923, 27891287, 753077249, 620192080073207, 40644910035811590827, 21600371677519118879091707, 67501161497474683459322666743, 19258869155079686765079369534624940189973
Offset: 0

Views

Author

Amarnath Murthy, May 04 2001

Keywords

Examples

			1, 5/4, 139/108, 8923/6912,...
		

Crossrefs

Cf. A061464.

Programs

  • Maple
    summ := 0; for n from 1 to 15 do printf("%d ", numer(summ)); if (1 = 1) then summ := summ + 1/n^n: end if; od;
  • Mathematica
    Join[{0},Accumulate[Table[1/n^n,{n,15}]]]//Numerator (* Harvey P. Dale, Jul 26 2018 *)

Extensions

More terms from Winston C. Yang (winston(AT)cs.wisc.edu), May 19 2001

A357557 a(n) is the numerator of the coefficient c in the polynomial of the form y(x)=x^n+c such that starting with y(x)=x for n=1 each polynomial is C-1 continuous with the previous one.

Original entry on oeis.org

0, 1, 43, 3481, 12647597, 380547619, 340607106994117, 23867104301800579837, 13408353860832026243555117, 43926321999197203038889578577, 13055436009603783636664151666161626100547, 6766346844526064783736339920897644104961
Offset: 1

Views

Author

Inigo Quilez, Oct 03 2022

Keywords

Comments

The polynomials y(x)=x^n+c(n) can only be connected at x=n/(n+1) and with coefficients c(n) = { 0, 1/4, 43/108, 3481/6912, ... }. The denominator of c(n) is A061464. The numerator is our sequence a(n)

Crossrefs

Cf. A061464 (denominators).

Programs

  • PARI
    a(n) = my(p=1); numerator(sum(i=2,n, p/(p=i^i))); \\ Kevin Ryde, Oct 03 2022

Formula

a(n) = numerator of Sum_{i=1..n} (i^i)/((i+1)^(i+1)).

A120264 Numerator of Sum_{k=1..n} (-1)^(k+1)/k^k.

Original entry on oeis.org

1, 3, 85, 5413, 16922537, 456895999, 376274084904457, 24659496552164597077, 13105067550356276873597957, 40953336089635928267832533257, 11684464736880059106484670339210887010027
Offset: 1

Views

Author

Alexander Adamchuk, Jun 30 2006

Keywords

Comments

Denominator of Sum_{k=1..n} (1/k^k)*(-1)^(k+1) is A061464(n).
Sum_{k>=1} (-1)^(k+1)/k^k = Integral_{x=0..1} x^x dx = 0.7834305107121344... A083648(n) gives its decimal expansion {7, 8, 3, 4, 3, 0, 5, 1, 0, 7, 1, 2, 1, 3, 4, 4, 0, 7, 0, 5, 9, ...}. - Alexander Adamchuk, Aug 21 2006

Crossrefs

Programs

  • Mathematica
    Numerator[Table[Sum[1/k^k*(-1)^(k+1),{k,1,n}],{n,1,20}]]

Formula

a(n) = numerator(Sum_{k=1..n} (1/k^k)*(-1)^(k+1)).
Showing 1-3 of 3 results.