|
|
A298527
|
|
Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n+1)*g), where g = 1.9078532620869538..., s(n) = (s(n - 1) + sqrt(3))^(1/2), s(0) = 2.
|
|
3
|
|
|
1, 2, 4, 6, 5, 3, 1, 3, 8, 3, 4, 6, 9, 9, 0, 9, 5, 8, 3, 2, 5, 7, 4, 3, 8, 5, 5, 2, 3, 6, 3, 6, 2, 8, 3, 3, 5, 7, 5, 8, 0, 1, 3, 5, 9, 2, 0, 4, 9, 6, 8, 0, 5, 6, 7, 5, 2, 9, 6, 9, 1, 1, 6, 2, 0, 0, 7, 6, 0, 3, 3, 9, 3, 6, 2, 5, 0, 6, 4, 5, 5, 9, 3, 8, 9, 8
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
(lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - sqrt(3). See A298512 for a guide to related sequences.
|
|
LINKS
|
|
|
EXAMPLE
|
s(0) + s(1) + ... + s(n) - (n+1)*g -> 0.124653138346990958325743855236362833575...
|
|
MATHEMATICA
|
s[0] = 2; d = Sqrt[3]; 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]] (* A298527 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|