A298527 Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n+1)*g), where g = 1.9078532620869538..., s(n) = (s(n - 1) + sqrt(3))^(1/2), s(0) = 2.

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

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..85.

Example

s(0) + s(1) + ... + s(n) - (n+1)*g -> 0.124653138346990958325743855236362833575...

Mathematica

s[0] = 2; 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]] (* A298527 *)

Crossrefs

Cf. A298512, A298526.

Sequence in context: A082747 A127275 A242796 * A071288 A063892 A353650

Adjacent sequences: A298524 A298525 A298526 * A298528 A298529 A298530

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 12 2018

Status

approved