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 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. 3
 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, 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, 0, 8, 7, 6, 5, 5, 3, 1, 0, 3, 7, 2, 0, 3, 7, 0, 3, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 -> 1.928338346029993604661257220820526670... MATHEMATICA s[0] = 3; 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]];  (* A298514 *) CROSSREFS Cf. A001622, A298512, A298513. Sequence in context: A019733 A111722 A217054 * A137301 A299957 A252001 Adjacent sequences:  A298511 A298512 A298513 * A298515 A298516 A298517 KEYWORD nonn,easy,cons AUTHOR Clark Kimberling, Feb 11 2018 STATUS approved

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Last modified January 17 15:12 EST 2020. Contains 330958 sequences. (Running on oeis4.)