A298526 Decimal expansion of lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 1.9078532620869538..., s(n) = (s(n - 1) + sqrt(3))^(1/2), s(0) = 1.

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

Offset: 1

Author

Clark Kimberling, Feb 12 2018

Keywords

• nonn
• easy
• cons

Comments

(lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - sqrt(3). See A298512 for a guide to related sequences.

Examples

			(n+1)*g - s(0) - s(1) - ... - s(n) -> 1.255130808144253924335186404635816957676...
		

Crossrefs

Cf. A298512, A298527.

Programs

Mathematica

s[0] = 1; d = Sqrt[3]; 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]] (* A298526 *)