This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A298512 #11 Jan 10 2024 16:06:25
%S A298512 9,1,5,0,4,9,8,4,8,0,1,5,1,3,4,9,1,4,8,4,3,6,3,1,2,1,4,6,0,3,0,0,2,1,
%T A298512 1,6,7,5,0,8,3,2,5,8,7,5,6,6,7,0,1,2,6,4,2,9,4,8,1,6,8,0,1,4,3,8,6,5,
%U A298512 7,6,0,3,7,9,2,8,5,2,4,1,7,4,6,3,6,2
%N A298512 Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) - s(1) - ... - s(n)), where g = (1 + sqrt (5))/2, s(n) = (s(n - 1) + 1)^(1/2), s(0) = 1.
%C A298512 Lim_{n->oo} s(n) = g = golden ratio, A001622. In the following guide to related sequences, the sequence gives the decimal expansion for lim_{n->oo} |(n+1)*g - s(0) - s(1) - ... - s(n)|, where s(n) = (s(n-1) + d)^p, and tau = (1+sqrt(5))/2.
%C A298512 ***
%C A298512 sequence d p a(0) g
%C A298512 A298512 1 1/2 1 (1+sqrt(5))/2
%C A298512 A298513 1 1/2 2 (1+sqrt(5))/2
%C A298512 A298514 1 1/2 3 (1+sqrt(5))/2
%C A298512 A298515 1/2 1/2 1 (1+sqrt(3))/2
%C A298512 A298516 2 1/2 1 2
%C A298512 A298517 3 1/2 1 (1+sqrt(13))/2
%C A298512 A298518 1 1/3 1 1.3247...
%C A298512 A298519 1 1/3 2 1.3247...
%C A298512 A298520 1 1/3 3 1.3247...
%C A298512 A298521 1 2/3 1 2.1478...
%C A298512 A298522 tau 1/2 1 1.8667...
%C A298512 A298523 tau 1/2 2 1.8667...
%C A298512 A298524 sqrt(2) 1/2 1 1.7900...
%C A298512 A298525 sqrt(2) 1/2 2 1.7900...
%C A298512 A298526 sqrt(3) 1/2 1 1.9078...
%C A298512 A298527 sqrt(3) 1/2 2 1.9078...
%C A298512 A298528 e 1/2 1 2.2228...
%C A298512 A298529 e 1/2 e 2.2228...
%C A298512 A298530 Pi 1/2 1 2.3416...
%C A298512 A298531 Pi 1/2 Pi 2.3416...
%C A298512 A298532 tau 1/2 tau 2.3416...
%e A298512 s(n) = (1, 1.4142..., 1.5537..., 1.5980..., 1.6118..., ...) with limit g = 1.618... = (1+sqrt(5))/2.
%e A298512 ((n + 1)*g - s(0) - s(1) - ... - s(n)) -> 0.9150498480151349148436312146030...
%t A298512 s[0] = 1; d = 1; p = 1/2; s[n_] := s[n] = (s[n - 1] + d)^p
%t A298512 N[Table[s[n], {n, 0, 30}]]
%t A298512 z = 200 ; g = GoldenRatio; s = N[(z + 1)*g - Sum[s[n], {n, 0, z}], 150 ];
%t A298512 RealDigits[s, 10][[1]]; (* A298512 *)
%Y A298512 Cf. A001622, A298513, A298514.
%K A298512 nonn,easy,cons
%O A298512 0,1
%A A298512 _Clark Kimberling_, Feb 11 2018