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.

A296301 Decimal expansion of Product_{k>=2} k^(1/k!).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Dec 09 2017

Keywords

Examples

			1.8290246795635718643895723573648858491007676333721141167306441...

Links

Crossrefs

Cf. A112302, A115522, A123852, A188835, A259235.

Programs

  • Mathematica
    RealDigits[Exp[Sum[ Log[k]/k!, {k, 2, 700}]], 10, 100][[1]] (* G. C. Greubel, Jul 28 2018 *)
  • PARI
    exp(suminf(k=2, log(k)/k!)) \\ Michel Marcus, Dec 11 2017

Formula

Equals (2*(3*(4*(5*(6*(7*...)^(1/7))^(1/6))^(1/5))^(1/4))^(1/3))^(1/2).
Equals exp(Sum_{k>=2} log(k)/k!).
Equals lim_{k->infinity} b(k)^(1/k!), where b(k) = k*b(k-1)^k with b(0) = 1.
Equals Product_{p prime} p^(Sum_{k>=2} (p-adic valuation of k)/k!).

A188834 Decimal expansion of limit sqrt(2*sqrt(4*sqrt(6*sqrt(8*sqrt(10*...sqrt(2*n...)))))).

Original entry on oeis.org

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

Views

Author

Paolo P. Lava, Apr 12 2011

Keywords

Examples

			3.3233758992671882...

Links

Crossrefs

Cf. A112302, A171759, A188835.

Programs

  • Maple
    with(numtheory);
P:=proc(i)
local a,n;
a:=1;
for n from i by -1 to 1 do a:=2*n*sqrt(a); od;
print(evalf(sqrt(a),1000));
end:
P(5000);
  • Mathematica
    digits = 101; p[m_] := p[m] = Fold[N[Sqrt[#2*#1], digits] &, 1, Range[2*m, 2, -2]] // RealDigits[#, 10, digits]& // First; p[digits]; p[m = 2*digits]; While[p[m] != p[m/2], m = 2*m]; p[m] (* Jean-François Alcover, Feb 24 2014 *)

A190142 Decimal expansion of limit sqrt(2’*sqrt(3’*sqrt(4’*sqrt(5’*sqrt(6’*...))))), where n’ is the arithmetic derivative of n.

Original entry on oeis.org

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

Views

Author

Paolo P. Lava, May 05 2011

Keywords

Examples

			1.29134317210725954613882...

Crossrefs

Cf. A003415, A112302, A171759, A188834, A188835.

Programs

  • Maple
    with(numtheory);
P:=proc(i)
local a,f,n,p,pfs;
a:=1;
for n from i by -1 to 2 do
  pfs:=ifactors(n)[2];
  f:=n*add(op(2,p)/op(1,p),p=pfs) ;
  a:=f*sqrt(a);
od;
print(evalf(sqrt(a),150));
end:
P(500);
  • Mathematica
    digits = 105; d[0] = d[1] = 0; d[n_] := d[n] = n*Total[Apply[#2/#1 &, FactorInteger[n], {1}]]; f[n_] := f[n] = Fold[Sqrt[d[#2]*#1]&, n, Range[n-1, 2, -1]] // RealDigits[#, 10, digits]& // First; f[digits]; f[n = 2*digits]; While[f[n] != f[n/2], n = 2*n]; f[n] (* Jean-François Alcover, Feb 21 2014 *)
Showing 1-3 of 3 results.

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