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Search: id:A019529
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| A019529 |
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Sum of a(n) terms of 1/sqrt(k) first strictly exceeds n. |
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+0
13
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| 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; listen)
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OFFSET
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0,2
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EXAMPLE
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Let b(k) = 1 + 1/sqrt(2) + 1/sqrt(3) + ... + 1/sqrt(k):
.k.......1....2.....3.....4.....5.....6.....7
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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
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MATHEMATICA
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s = 0; k = 1; Do[ While[ s <= n, s = s + N[ 1/Sqrt[ k ], 24 ]; k++ ]; Print[ k - 1 ], {n, 1, 75} ]
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CROSSREFS
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A054040 is another version. See also A002387, A004080.
Sequence in context: A064480 A115024 A167050 this_sequence A130053 A025488 A088585
Adjacent sequences: A019526 A019527 A019528 this_sequence A019530 A019531 A019532
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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Edited by N. J. A. Sloane, Sep 01 2009
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