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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A238799 a(0) = 1, a(n+1) = 2*a(n)^3 + 3*a(n).

Original entry on oeis.org

1, 5, 265, 37220045, 103124220135120334842385, 2193370648451279691104497113491599222165108730278225579497595691360405
Offset: 0

Views

Author

Arkadiusz Wesolowski, Mar 05 2014

Keywords

Comments

a(6) has 209 digits and is too large to include.
Except for the first term, this is a subsequence of A175180.
The squares larger than 1 are in A076445.
If we define u(0) = 1 , u(n+1) = (u(n)/3)*(u(n)^2+9) / (u(n)^2 + 1), then u(n) = a(n) / A378683(n) ; this is Halley's method to calculate sqrt(3). - Robert FERREOL, Dec 21 2024

Links

Crossrefs

Cf. A175180, A378683.

Programs

  • Mathematica
    RecurrenceTable[{a[0] == 1, a[n] == 2*a[n - 1]^3 + 3*a[n - 1]}, a[n], {n, 5}]
NestList[2#^3+3#&,1,5] (* Harvey P. Dale, Mar 22 2023 *)
  • PARI
    a=1; print1(a, ", "); for(n=1, 5, b=2*a^3+3*a; print1(b, ", "); a=b);
  • PARI
    { A238799(n) = my(q=Mod(x,x^2-3)); lift( (1+q)*(2+q)^((3^n-1)/2) + (1-q)*(2-q)^((3^n-1)/2) )/2; } \\ Max Alekseyev, Sep 04 2018

Formula

a(n) = sqrt(2) * sinh( 3^n * arcsinh(1/sqrt(2)) ) = (1+sqrt(3))/2 * (2+sqrt(3))^((3^n-1)/2) + (1-sqrt(3))/2 * (2-sqrt(3))^((3^n-1)/2). - Max Alekseyev, Sep 04 2018
a(n) = ((1 + sqrt(3))^(3^n) + (1 - sqrt(3))^(3^n))/2^((3^n+1)/2) = A002531(3^n) = A080040(3^n)/2^((3^n+1)/2). - Robert FERREOL, Nov 19 2024
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