A298532 Decimal expansion of lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 1.866760399173862092990..., s(n) = (s(n - 1) + tau)^(1/2), s(0) = tau = (1+sqrt(5))/2 (golden ratio).

3, 4, 1, 5, 3, 3, 3, 9, 8, 0, 5, 2, 9, 0, 5, 7, 3, 2, 1, 9, 5, 0, 4, 3, 4, 3, 7, 0, 6, 6, 2, 3, 3, 3, 0, 6, 0, 7, 7, 0, 1, 2, 2, 2, 7, 4, 7, 1, 1, 6, 1, 5, 0, 3, 8, 9, 0, 1, 9, 9, 5, 2, 7, 0, 5, 0, 4, 8, 6, 6, 6, 5, 4, 5, 1, 9, 1, 9, 1, 7, 3, 0, 0, 2, 4, 5

Offset: 0

Author

Clark Kimberling, Feb 13 2018

Keywords

• nonn
• easy
• cons

Comments

(lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - tau. See A298512 for a guide to related sequences.

Examples

			lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)) -> 0.3415333980529057321950...
		

Crossrefs

Cf. A298512, A298531.

Programs

Mathematica

tau = GoldenRatio;
s[0] = tau; d = tau; p = 1/2;
g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
RealDigits[s, 10][[1]] (* A298532 *)