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 A298515 Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) -s(1) - ... - s(n)), where g = (1 + sqrt (3))/2, s(n) = ((s(n - 1) + 1/2)^(1/2), s(0) = 1. 3
 5, 9, 0, 7, 3, 1, 6, 8, 1, 5, 1, 8, 0, 7, 7, 5, 7, 4, 1, 8, 5, 9, 7, 9, 5, 1, 7, 6, 8, 4, 1, 9, 4, 7, 8, 7, 9, 3, 0, 3, 2, 4, 0, 0, 1, 2, 4, 1, 6, 7, 7, 9, 9, 7, 1, 2, 9, 7, 8, 1, 6, 3, 6, 7, 0, 4, 9, 8, 3, 9, 7, 7, 8, 6, 4, 2, 9, 8, 2, 4, 5, 8, 0, 0, 1, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS (lim_ {n->oo} s(n)) = g = (1 + sqrt (3))/2.  See A298512 for a guide to related sequences. LINKS EXAMPLE s(n) -> g = (1+sqrt(3))/2. (n+1)*g - s(0) - s(1) - ... - s(n) -> 0.590731681518077574185979517684194787... MATHEMATICA s[0] = 1; d = 1/2; 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 ]; StringJoin[StringTake[ToString[s], 41], "..."] RealDigits[s, 10][[1]]   (* A298515 *) CROSSREFS Cf. A298512, A298516, A298517. Sequence in context: A096789 A342714 A261623 * A306778 A019705 A269957 Adjacent sequences:  A298512 A298513 A298514 * A298516 A298517 A298518 KEYWORD nonn,easy,cons AUTHOR Clark Kimberling, Feb 11 2018 STATUS approved

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Last modified December 5 06:30 EST 2021. Contains 349532 sequences. (Running on oeis4.)