A298517 - OEIS

A298517

Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) - s(1) - ... - s(n)), where g = (1 + sqrt (13))/2, s(n) = (s(n - 1) + 3)^(1/2), s(0) = 1.

%I #6 Jan 10 2024 16:08:38

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

%T 8,8,5,9,9,4,2,5,2,6,7,7,7,2,8,7,6,9,5,3,6,9,7,6,6,3,8,6,1,9,4,7,9,2,

%U 4,1,7,3,1,4,3,9,5,2,3,3,5,3,3,4,9,0

%N Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) - s(1) - ... - s(n)), where g = (1 + sqrt (13))/2, s(n) = (s(n - 1) + 3)^(1/2), s(0) = 1.

%C (lim_ {n->oo} s(n)) = g = (1 + sqrt (13))/2. See A298512 for a guide to related sequences.

%e ((n + 1)*g - s(0) - s(1) - ... - s(n)) -> 0.91504984801513491484363121460300...

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

%t N[Table[s[n], {n, 0, 30}]]

%t z = 200 ; g = (1 + Sqrt[13])/2;

%t s = N[(z + 1)*g - Sum[s[n], {n, 0, z}], 150 ];

%t RealDigits[s, 10][[1]]; (* A298517 *)

%Y Cf. A298512, A298515, A298516.

%K nonn,easy,cons

%O 0,2

%A _Clark Kimberling_, Feb 11 2018