A370869 a(0) = 0; thereafter, a(n) = a(n-1)^2 - 3*A058891(n).

0, -3, 3, -15, -159, -73023, -1110092415, -26437810940723795199, 188534296956047109666345322462443132417, -138142952727263338693771981084959537243558105718529460985143718744222698198015

Offset: 0

Author

Giorgos Kalogeropoulos, Mar 03 2024

Keywords

• sign

Comments

Numerators in the iteration f(0) = 0 and f(n) = f(n-1)^2 - 3/2. First values are 0, -3/2, 3/4, -15/16, -159/256, ... Denominators are A001146(n). We still don't know the behavior of this iteration (see links).

Links

• Jordana Cepelewicz, ‘Entropy Bagels’ and Other Complex Structures Emerge From Simple Rules, Quanta Magazine, 27 February 2024.
• Holly Krieger and Brady Haran, The Mystery of Hyperbolicity, Numberphile video (2024).

Crossrefs

Cf. A058891, A001146.

Programs

Mathematica

a[0]=0; a[n_]:=a[n]=a[n-1]^2-3*2^(2^(n-1)- 1); Array[a,9,0]

Formula

a(n) = a(n-1)^2 - 3*A058891(n).