A298516 Decimal expansion of lim_ {n->oo} (2n+2 - s(0) - s(1) - ... - s(n)), where s(n) = (s(n - 1) + 2)^(1/2), s(0) = 1.

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

Offset

1,2

Comments

See A298512 for a guide to related sequences.

Links

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

Example

2n + 2 - s(0) - s(1) - ... - s(n) -> 1.358917762842788340395837672187105945234...

Mathematica

s[0] = 1; d = 2; 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 ];
StringJoin[StringTake[ToString[s], 41], "..."]
u = RealDigits[s, 10][[1]]   (* A298516 *)

Crossrefs

Cf. A298512, A298516, A298517.

Sequence in context: A354415 A186697 A077523 * A157291 A107820 A191931

Adjacent sequences: A298513 A298514 A298515 * A298517 A298518 A298519

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 11 2018

Status

approved