A004081 -id:A004081 - cp's OEIS frontend

A226190 Least positive integer k such that 1 + 1/2 + ... + 1/k >= log(n).

1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 26, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 38, 38, 39, 39, 40, 40, 41, 42, 42, 43, 43, 44, 44, 45

Offset: 1

Clark Kimberling, May 30 2013

nonn

			a(9) = 5 because 1 + 1/2 + 1/3 + 1/4 < log(9) < 1 + 1/2 + 1/3 + 1/4 + 1/5.

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A226183, A226189, A004081.

z = 80; f[n_] := 1/n; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) > Log[n] &], {n, 1, z}]; m = Map[a, Range[z]]

A127264 Nearest integer to 2*(Sum_{i=1..10^n/2} 1/i) - 1.

Original entry on oeis.org

4, 8, 13, 17, 22, 26, 31, 36, 40, 45, 49, 54, 59, 63, 68, 72, 77, 82, 86, 91, 95, 100, 105, 109, 114, 119, 123, 128, 132, 137, 142, 146, 151, 155, 160, 165, 169, 174, 178, 183, 188, 192, 197, 201, 206, 211, 215, 220, 224, 229, 234, 238, 243, 247, 252, 257, 261, 266, 270, 275

Offset: 1

Ben Paul Thurston, Mar 27 2007

nonn

The original definition was: Nearest integer to Sum[(10^n-i)/i,{i,1,10^n/2}]/(10^n/2), but this was simplified to the present definition by Jon E. Schoenfield, Aug 05 2008.

			a(1)=4 because round((9/1 + 8/2 + 7/3 + 6/4 + 5/5)/5) is 4.
a(2)=8 because round((99/1 + 98/2 + ... + 50/50))/50 is 8.

Jon E. Schoenfield, Table of n, a(n) for n = 1..1000

Different from A004081, although the sequences have the same first few terms.

for i from 10 to 11 by 2 do s:=0; t:=0; for d from i/2 to i -1 do s:= s + (d / (i - d)); t:= t +1; end do; print(round((s / t))); end do;

Table[Round[-1 + 2*HarmonicNumber[Floor[10^n/2]]], {n, 1, 50}] (* G. C. Greubel, Aug 31 2018 *)

a(n)={ my(i,a=0); for(i=1, 10^n/2, a += 1/i); return(round(2*a-1)); }
main(size)={return(vector(size,m,a(m)));} /* Anders Hellström, Jul 12 2015 */

a(n) = round(2 * (log(m) + Gamma) + 1/m - ...) - 1 where m = 10^n / 2 and Gamma = 0.57721566490153286... (the Euler-Mascheroni constant A001620). - Jon E. Schoenfield, Aug 05 2008

Extended and edited by John W. Layman, Jul 10 2007

Terms from a(11) onwards from Jon E. Schoenfield, Aug 05 2008

cp's OEIS Frontend

A226190 Least positive integer k such that 1 + 1/2 + ... + 1/k >= log(n).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

A127264 Nearest integer to 2*(Sum_{i=1..10^n/2} 1/i) - 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

Extensions