A242679 Bobo numbers: Numbers k with the property that floor(e*k) = least m with Sum_{j=k..m} 1/j > 1.

4, 11, 18, 25, 32, 36, 43, 50, 57, 64, 71, 75, 82, 89, 96, 103, 114, 121, 128, 135, 142, 146, 153, 160, 167, 174, 185, 192, 199, 206, 213, 217, 224, 231, 238, 245, 256, 263, 270, 277, 284, 288, 295, 302, 309, 316, 327, 334, 341, 348, 355, 359, 366, 373, 380, 387, 398, 405, 412, 419, 426, 430, 437, 444, 451, 458, 469, 476, 483, 490, 497

Offset

1,1

Comments

These are the numbers n for which A103762(n) = floor(e*n).

If frac(e*n) > (e-1)/2, then n is a Bobo number, but not every Bobo number has this property. The exceptions are in A277603.

In Bobo's article (see Bobo link), the Bobo numbers through 2105 are listed. There is a typo: the number 143 is given in place of the correct number 142.

These numbers are mentioned in the comments associated with A103762. Differences between consecutive Bobo numbers are indeed 4, 7, or 11. An elementary proof is given in the Clancy/Kifowit link.

Links

Steven J. Kifowit, Table of n, a(n) for n = 1..10000

E. R. Bobo, A sequence related to the harmonic series, College Math. J. 26 (1995), 308-310.

D. T. Clancy and S. J. Kifowit, A closer look at Bobo's sequence, College Math. J. 45 (2014), 199-206.

Steve Kifowit, Bobo Numbers, Bobbers, and Bears—Experiences, Undergraduate Research, Preprint, 2016.

Prog

(PARI) is(n)=my(e=exp(1), s); if(frac(e*n)>(e-1)/2, return(1)); s=sum(j=n, e*n\1-1, 1/j); s<=1 && s+e*n\1>1 \\ Charles R Greathouse IV, Sep 17 2016

Crossrefs

Cf. A103762, A277603.

Sequence in context: A025403 A047703 A339215 * A017029 A009873 A300744

Adjacent sequences: A242676 A242677 A242678 * A242680 A242681 A242682

Keyword

nonn

Author

Steven J. Kifowit, May 20 2014

Status

approved