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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. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

(lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - sqrt(2).  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 -> 0.289932185664479574074147512346151058813...

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 *)

CROSSREFS

Cf. A298512, A298524.

Sequence in context: A021349 A145426 A200499 * A081101 A043059 A237415

Adjacent sequences:  A298522 A298523 A298524 * A298526 A298527 A298528

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Feb 12 2018

STATUS

approved

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Last modified April 20 12:44 EDT 2021. Contains 343135 sequences. (Running on oeis4.)