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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A258112 Decimal expansion of a constant related to A001056.

Original entry on oeis.org

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

Views

Author

Vaclav Kotesovec, May 20 2015

Keywords

Examples

			1.7978784900091604813559508837031352161793665265019525368552362542745...

Crossrefs

Cf. A001056, A076949, A258113.

Programs

  • Mathematica
    A001056 = RecurrenceTable[{a[0]==1, a[1]==N[3, 200], a[n] == a[n-1]*a[n-2]+1}, a[n], {n, 1, 30}]; Do[Print[N[Exp[c2]/.Solve[Table[Log[A001056[[n]]] == c1*((1-Sqrt[5])/2)^n + c2*((1+Sqrt[5])/2)^n, {n, k, k+1}]], 120][[1]]], {k, Length[A001056]-2, Length[A001056]-1}];

Formula

Equals limit n->infinity (A001056(n))^((2/(1+sqrt(5)))^n).

A133400 a(0)=a(1)=a(2) = 1, thereafter a(n) = a(n-1)*a(n-2)*a(n-3) + 1.

Original entry on oeis.org

1, 1, 1, 2, 3, 7, 43, 904, 272105, 10577265561, 2601826668310218121, 7488387181338771882437732599874506, 206081999881071045385328009597554265108557649484947339933019787
Offset: 0

Views

Author

Jonathan Vos Post, Nov 24 2007, Nov 26 2007

Keywords

Comments

A tribonacci analog of A001056.
a(13) has 115 digits. - R. J. Mathar, Dec 10 2007

Examples

			a(8) = a(7)*a(6)*a(5) + 1 = 904 * 43 * 7 + 1 = 272105.
a(9) ~ 2.60182667 * 10^18.
a(10) ~ 7.48838719 * 10^33.
a(11) ~ 2.06082 * 10^62.

Links

Crossrefs

Cf. A001056, A007660, A058265.

Programs

  • GAP
    a:=[1,1,1];; for n in [4..15] do a[n]:=a[n-1]*a[n-2]*a[n-3]+1; od; a; # G. C. Greubel, Sep 20 2019
  • Magma
    I:=[1,1,1]; [n le 3 select I[n] else Self(n-1)*Self(n-2)* Self(n-3) + 1: n in [1..15]]; // G. C. Greubel, Sep 20 2019
  • Maple
    A133400 := proc(n) local i ; if n <= 2 then 1; else 1+mul( A133400(i),i=n-3..n-1) ; fi ; end: seq(A133400(n),n=0..15) ; # R. J. Mathar, Dec 10 2007
  • Mathematica
    RecurrenceTable[{a[0]==1,a[1]==1,a[2]==1, a[n] == a[n-1]*a[n-2]*a[n-3] + 1},a,{n,0,15}] (* Vaclav Kotesovec, May 05 2015 *)
nxt[{a_,b_,c_}]:={b,c,a*b*c+1}; NestList[nxt,{1,1,1},15][[All,1]] (* Harvey P. Dale, Mar 05 2017 *)
  • PARI
    m=15; v=concat([1,1,1], vector(m-3)); for(n=4, m, v[n]=v[n-1]*v[n-2] *v[n-3] +1 ); v \\ G. C. Greubel, Sep 20 2019
  • Sage
    def a(n):
    if (n<3): return 1
    else: return a(n-1)*a(n-2)*a(n-3) + 1
[a(n) for n in (0..15)] # G. C. Greubel, Sep 20 2019

Formula

a(n) ~ c^(t^n), where c = 1.1004451797920944914628..., t = A058265 = 1.8392867552141611325518... . - Vaclav Kotesovec, May 05 2015

Extensions

More terms from R. J. Mathar, Dec 10 2007
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