cp's OEIS Frontend

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.

%I A298514 #6 Jan 10 2024 16:07:31
%S A298514 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,
%T A298514 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,
%U A298514 0,8,7,6,5,5,3,1,0,3,7,2,0,3,7,0,3,4
%N 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.
%C A298514 (lim_ {n->oo} s(n)) = g = golden ratio, A001622.  See A298512 for a guide to related sequences.
%e A298514 s(n) -> g = (1+sqrt(5))/2, as at A001622.
%e A298514 s(0) + s(1) + ... + s(n) - (n + 1)*g -> 1.928338346029993604661257220820526670...
%t A298514 s[0] = 3; d = 1; p = 1/2; s[n_] := s[n] = (s[n - 1] + d)^p
%t A298514 N[Table[s[n], {n, 0, 30}]]
%t A298514 z = 200 ; g = GoldenRatio; s = N[-(z + 1)*g + Sum[s[n], {n, 0, z}], 150 ];
%t A298514 RealDigits[s, 10][[1]];  (* A298514 *)
%Y A298514 Cf. A001622, A298512, A298513.
%K A298514 nonn,easy,cons
%O A298514 1,2
%A A298514 _Clark Kimberling_, Feb 11 2018