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

Author

Steven J. Kifowit, May 20 2014

Keywords

• nonn

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.

Crossrefs

Cf. A103762, A277603.

Programs

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