A298513 Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n + 1)*g), where g = (1 + sqrt (5))/2, s(n) = (s(n - 1) + 1)^(1/2), s(0) = 2.

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

Offset

0,1

Comments

(lim_ {n->oo} s(n)) = g = golden ratio, A001622. See A298512 for a guide to related sequences.

Links

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

Example

s(n) -> g = (1+sqrt(5))/2, as at A001622.
s(0) + s(1) + ... + s(n) - (n + 1)*g -> 0.54637233477988845286584405518616478...

Mathematica

s[0] = 2; d = 1; p = 1/2; s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
z = 200 ; g = GoldenRatio; s = N[-(z + 1)*g + Sum[s[n], {n, 0, z}], 150 ];
RealDigits[s, 10][[1]];  (* A298513 *)

Crossrefs

Cf. A001622, A298512, A298514.

Sequence in context: A190613 A161011 A232734 * A021187 A075194 A328263

Adjacent sequences: A298510 A298511 A298512 * A298514 A298515 A298516

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 11 2018

Status

approved