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 A019529 Sum of a(n) terms of 1/sqrt(k) first strictly exceeds n. 15
 1, 2, 3, 5, 7, 10, 14, 18, 22, 27, 33, 39, 45, 52, 60, 68, 76, 85, 95, 105, 115, 126, 138, 150, 162, 175, 189, 202, 217, 232, 247, 263, 280, 297, 314, 332, 351, 370, 389, 409, 430, 451, 472, 494, 517, 540, 563, 587, 612, 637, 662, 688, 715, 741, 769, 797, 825 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..56. EXAMPLE Let b(k) = 1 + 1/sqrt(2) + 1/sqrt(3) + ... + 1/sqrt(k): .k.......1....2.....3.....4.....5.....6.....7 ------------------------------------------------- b(k)...1.00..1.71..2.28..2.78..3.23..3.64..4.01 For A019529 we have: n=0: smallest k is a(0) = 1 since 1.00 > 0 n=1: smallest k is a(1) = 2 since 1.71 > 1 n=2: smallest k is a(2) = 3 since 2.28 > 2 n=3: smallest k is a(3) = 5 since 3.23 > 3 n=4: smallest k is a(4) = 7 since 4.01 > 4 For AA054040 we have: n=1: smallest k is a(1) = 1 since 1.00 >= 1 n=2: smallest k is a(2) = 3 since 2.28 >= 2 n=3: smallest k is a(3) = 5 since 3.23 >= 3 n=4: smallest k is a(4) = 7 since 4.01 >= 4 MATHEMATICA s = 0; k = 1; Do[ While[ s <= n, s = s + N[ 1/Sqrt[ k ], 24 ]; k++ ]; Print[ k - 1 ], {n, 1, 75} ] CROSSREFS A054040 is another version. See also A002387, A004080. Sequence in context: A115024 A167050 A308388 * A194242 A173538 A130053 Adjacent sequences: A019526 A019527 A019528 * A019530 A019531 A019532 KEYWORD nonn AUTHOR Robert G. Wilson v EXTENSIONS Edited by N. J. A. Sloane, Sep 01 2009 STATUS approved

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Last modified September 23 07:35 EDT 2023. Contains 365544 sequences. (Running on oeis4.)