

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.


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
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]]; (* A298514 *)


CROSSREFS

Cf. A001622, A298512, A298513.
Sequence in context: A019733 A111722 A217054 * A137301 A299957 A252001
Adjacent sequences: A298511 A298512 A298513 * A298515 A298516 A298517


KEYWORD

nonn,easy,cons


AUTHOR

Clark Kimberling, Feb 11 2018


STATUS

approved



