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 A298513 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) = 2. 3
 5, 4, 6, 3, 7, 2, 3, 3, 4, 7, 7, 9, 8, 8, 8, 4, 5, 2, 8, 6, 5, 8, 4, 4, 0, 5, 5, 1, 8, 6, 1, 6, 4, 7, 8, 8, 0, 2, 8, 7, 5, 4, 7, 7, 9, 2, 0, 6, 8, 8, 0, 6, 2, 4, 5, 6, 6, 9, 2, 0, 5, 5, 4, 4, 7, 9, 0, 6, 9, 2, 2, 8, 3, 4, 9, 9, 3, 9, 6, 5, 3, 4, 1, 0, 6, 2 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS (lim_ {n->oo} s(n)) = g = golden ratio, A001622.  See A298512 for a guide to related sequences. LINKS EXAMPLE s(n) -> g = (1+sqrt(5))/2, as at A001622. s(0) + s(1) + ... + s(n) - (n + 1)*g -> 0.54637233477988845286584405518616478... MATHEMATICA s[0] = 2; d = 1; p = 1/2; s[n_] := s[n] = (s[n - 1] + d)^p N[Table[s[n], {n, 0, 30}]] z = 200 ; g = GoldenRatio; s = N[-(z + 1)*g + Sum[s[n], {n, 0, z}], 150 ]; RealDigits[s, 10][[1]];  (* A298513 *) CROSSREFS Cf. A001622, A298512, A298514. Sequence in context: A190613 A161011 A232734 * A021187 A075194 A328263 Adjacent sequences:  A298510 A298511 A298512 * A298514 A298515 A298516 KEYWORD nonn,easy,cons AUTHOR Clark Kimberling, Feb 11 2018 STATUS approved

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Last modified September 20 10:51 EDT 2021. Contains 347584 sequences. (Running on oeis4.)