A298531 Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n+1)*g), where g = 2.3416277185114784317..., s(n) = (s(n - 1) + Pi)^(1/2), s(0) = Pi.

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

Offset

1,4

Comments

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

Links

Table of n, a(n) for n=1..86.

Example

lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n+1)*g) -> 1.009415125594648468509...

Mathematica

s[0] = Pi; d = Pi; 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]] (* A298531 *)

Crossrefs

Cf. A298512, A298530.

Sequence in context: A286229 A242611 A098454 * A154206 A349624 A094881

Adjacent sequences: A298528 A298529 A298530 * A298532 A298533 A298534

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 12 2018

Status

approved