A298530 Decimal expansion of lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 2.3416277185114784317..., s(n) = (s(n - 1) + Pi)^(1/2), s(0) = 1.

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

Offset: 1

Author

Clark Kimberling, Feb 12 2018

Keywords

• nonn
• easy
• cons

Comments

(lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - Pi. See A298512 for a guide to related sequences.

Examples

			lim_ {n->oo} ((n+1)*g-s(0)-s(1)-...-s(n)) -> 1.732644070061485804124716667...
		

Crossrefs

Cf. A298512, A298531.

Programs

Mathematica

s[0] = 1; d = Pi; 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]] (* A298530 *)