A006279 Denominators of convergents to Cahen's constant: a(n+2) = a(n)^2*a(n+1) + a(n). (Formerly M0914)

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

Offset

0,3

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.

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 *)

Prog

(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

Crossrefs

Cf. A118227, A006280, A006281.

Sequence in context: A294380 A343261 A308128 * A041521 A101003 A042071

Adjacent sequences: A006276 A006277 A006278 * A006280 A006281 A006282

Keyword

nonn,easy,frac

Author

N. J. A. Sloane.

Extensions

Definition clarified by Jonathan Sondow, Aug 20 2014

Status

approved