A123180 Even positions of Sylvester's sequence A000058; the denominators of the (greedy) Egyptian fraction expansion of Cahen's constant.

2, 7, 1807, 10650056950807, 12864938683278671740537145998360961546653259485195807

Offset

0,1

Links

Amiram Eldar, Table of n, a(n) for n = 0..6

Eugène Cahen, Note sur un développement des quantités numériques, qui présente quelque analogie avec celui en fractions continues, Nouvelles Annales de Mathématiques, Vol. 10 (1891), pp. 508-514.

Eric Weisstein's World of Mathematics, Cahen's Constant.

Wikipedia, Cahen's constant.

Formula

a(n) = a(n-1)*(a(n-1)-1)*(a(n-1)*(a(n-1)-1)+1)+1.

a(n) is approximately k^4^n with k = 1.5979102180318731783... (A077125). - Charles R Greathouse IV, Dec 12 2013

Sum_{n>=0} 1/a(n) = A118227. - Amiram Eldar, Mar 19 2024

Mathematica

f[n_] := n*(n-1)*(n*(n-1)+1)+1; a[0] = 2; a[n_] := a[n] = f[a[n-1]]; Array[a, 5, 0] (* Amiram Eldar, Mar 19 2024 *)
1+NestList[#(#+1)(#^2+#+1) &, 1, 4] (* Oliver Seipel, Aug 25 2024 *)

Prog

(PARI) a(n)=if(n, my(k=a(n-1)); k*=k-1; k*(k+1)+1, 2) \\ Charles R Greathouse IV, Dec 12 2013

Crossrefs

Cf. A000058, A006279, A006280, A006281, A077125, A118227.

Sequence in context: A000653 A128847 A144676 * A138198 A358482 A320505

Adjacent sequences: A123177 A123178 A123179 * A123181 A123182 A123183

Keyword

easy,nonn,changed

Author

David Eppstein, Oct 03 2006

Extensions

a(4) from Charles R Greathouse IV, Dec 12 2013

Status

approved