A298514 - OEIS

A298514

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) = 3.

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

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OFFSET

1,2

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=1..86.

EXAMPLE

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

s(0) + s(1) + ... + s(n) - (n + 1)*g -> 1.928338346029993604661257220820526670...

MATHEMATICA

s[0] = 3; d = 1; p = 1/2; s[n_] := s[n] = (s[n - 1] + d)^p