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%I #6 Jan 10 2024 16:15:59
%S 1,0,0,9,4,1,5,1,2,5,5,9,4,6,4,8,4,6,8,5,0,9,6,1,8,9,7,2,1,8,6,8,6,2,
%T 3,4,3,9,2,3,8,6,4,4,0,2,8,6,2,9,0,8,8,9,2,2,7,5,1,6,3,5,7,5,5,3,6,9,
%U 9,4,1,9,4,6,7,3,9,1,0,8,2,6,0,9,7,7
%N Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n+1)*g), where g = 2.3416277185114784317..., s(n) = (s(n - 1) + Pi)^(1/2), s(0) = Pi.
%C (lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - Pi. See A298512 for a guide to related sequences.
%e lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n+1)*g) -> 1.009415125594648468509...
%t s[0] = Pi; d = Pi; p = 1/2;
%t g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
%t s[n_] := s[n] = (s[n - 1] + d)^p
%t N[Table[s[n], {n, 0, 30}]]
%t s = N[Sum[-g + s[n], {n, 0, 200}], 150 ];
%t RealDigits[s, 10][[1]] (* A298531 *)
%Y Cf. A298512, A298530.
%K nonn,easy,cons
%O 1,4
%A _Clark Kimberling_, Feb 12 2018