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

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

1,1

Comments

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.

Links

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

Formula

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

Example

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.

Maple

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;

Mathematica

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

Prog

(PARI) 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 */

Crossrefs

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

Sequence in context: A311935 A311936 A004081 * A311937 A311938 A311939

Adjacent sequences: A127261 A127262 A127263 * A127265 A127266 A127267

Keyword

nonn

Author

Ben Paul Thurston, Mar 27 2007

Extensions

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

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

Status

approved