A006279 Denominators of convergents to Cahen's constant: a(n+2) = a(n)^2*a(n+1) + a(n).

1, 1, 2, 3, 14, 129, 25298, 420984147, 269425140741515486, 47749585090209528873482531562977121, 3466137915373323052799848584927709551269254572949111609037058632767202

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• frac

Comments

Shifted square roots of partial quotients in continued fraction expansion of Cahen's constant: a(n) = sqrt(A006280(n+2)). - Jonathan Sondow, Aug 20 2014

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Amiram Eldar, Table of n, a(n) for n = 0..13
• J. L. Davison and Jeffrey O. Shallit, Continued Fractions for Some Alternating Series, Monatshefte für Mathematik, Vol. 111 (1991), pp. 119-126; alternative link.

Crossrefs

Cf. A118227, A006280, A006281.

Programs

Maple

A006279 := proc(n) option remember; if n <= 1 then 1 else A006279(n-2)^2*A006279(n-1)+A006279(n-2) fi end:
seq(A006279(n), n=0..10);

Mathematica

a[n_] := a[n] = If[n < 2, 1, a[n-2]^2*a[n-1] + a[n-2]];
Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Sep 23 2022 *)

Python

from itertools import islice
def A006279_gen(): # generator of terms
    a, b = 1, 1
    yield a
    while True:
        yield b
        a, b = b, a*(a*b+1)
A006279_list = list(islice(A006279_gen(),10)) # Chai Wah Wu, Mar 19 2024

Extensions

Definition clarified by Jonathan Sondow, Aug 20 2014