A055937 a(n) = a(n-1) * a(n-2) - 1.

2, 2, 3, 5, 14, 69, 965, 66584, 64253559, 4278258972455, 274893365303916717344, 1176065006579831683931038116759519, 323292467474902888912311701915651931811127805144397535

Offset: 1

Author

Robert G. Wilson v, Jul 05 2000

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..19

Crossrefs

A152446 uses largest prime < a(n-1)*a(n-2) instead of subtracting 1. - Joshua D. Olson, Sep 29 2015

Cf. A007660, A121258.

Programs

Magma

I:=[2,2]; [n le 2 select I[n] else Self(n-1)*Self(n-2)-1: n in [1..15]]; // Vincenzo Librandi, Sep 30 2015

Mathematica

RecurrenceTable[{a[1]==a[2]==2, a[n]==a[n-1]*a[n-2] -1}, a, {n, 15}] (* Vincenzo Librandi, Sep 30 2015 *)
nxt[{a_,b_}]:={b,a*b-1}; NestList[nxt,{2,2},15][[All,1]] (* Harvey P. Dale, Dec 05 2020 *)

PARI

a(n) = if(n<3, 2, a(n-1)*a(n-2)-1);
vector(15, n, a(n)) \\ Altug Alkan, Sep 30 2015

Sage

@cached_function
def a(n):
    if n == 1 or n == 2:
        return 2
    else:
        return a(n - 1) * a(n - 2) - 1
[a(n) for n in range(1, 16)]  # G. C. Greubel, Jun 07 2019

Formula

a(n) ~ c^(phi^n), where c = 1.26679081808631741720378389711... and phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jun 15 2019