A019529 Sum of a(n) terms of 1/sqrt(k) first strictly exceeds n.

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

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 A054040 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} ]
With[{c=N[Accumulate[Table[1/Sqrt[x], {x, 1000}]]]}, Table[Position[c, _?(#>n&), 1, 1], {n, 0, 1000}]]//Flatten (* Harvey P. Dale, Mar 19 2025 *)

Crossrefs

A054040 is another version. See also A002387, A004080.

Sequence in context: A115024 A167050 A308388 * A397034 A194242 A173538

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