A298525 Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n+1)*g), where g = 1.790044015672757..., s(n) = (s(n - 1) + sqrt(2))^(1/2), s(0) = 2.

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

Offset: 0

Author

Clark Kimberling, Feb 12 2018

Keywords

• nonn
• easy
• cons

Comments

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

Examples

			s(0) + s(1) + ... + s(n) - (n+1)*g -> 0.289932185664479574074147512346151058813...
		

Crossrefs

Cf. A298512, A298524.

Programs

Mathematica

s[0] = 2; d = Sqrt[2]; 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]] (* A298525 *)