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Bobo numbers: Numbers k with the property that floor(e*k) = least m with Sum_{j=k..m} 1/j > 1.
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%I #37 Feb 14 2021 13:01:03

%S 4,11,18,25,32,36,43,50,57,64,71,75,82,89,96,103,114,121,128,135,142,

%T 146,153,160,167,174,185,192,199,206,213,217,224,231,238,245,256,263,

%U 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

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

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

%C 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.

%C 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.

%C 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.

%H Steven J. Kifowit, <a href="/A242679/b242679.txt">Table of n, a(n) for n = 1..10000</a>

%H E. R. Bobo, <a href="http://www.jstor.org/stable/2687034">A sequence related to the harmonic series</a>, College Math. J. 26 (1995), 308-310.

%H D. T. Clancy and S. J. Kifowit, <a href="http://dx.doi.org/10.4169/college.math.j.45.3.199">A closer look at Bobo's sequence</a>, College Math. J. 45 (2014), 199-206.

%H Steve Kifowit, <a href="http://stevekifowit.com/pubs/denver.pdf">Bobo Numbers, Bobbers, and Bears—Experiences</a>, Undergraduate Research, Preprint, 2016.

%o (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

%Y Cf. A103762, A277603.

%K nonn

%O 1,1

%A _Steven J. Kifowit_, May 20 2014