A277603 Exceptional Bobo numbers: terms of A242679 that satisfy frac[e*A242679(n)]<(e-1)/2.

36, 9045, 5195512, 5311399545, 8488859795196, 25466579385587, 19542965851120621, 58628897553361862, 61250772004870841520, 183752316014612524559, 250769086731739376780337, 752307260195218130341010, 1299515735021702625544976020, 3898547205065107876634928059

Offset: 1

Author

Steven J. Kifowit, Oct 22 2016

Keywords

• nonn

Comments

The exceptional Bobo numbers (EBNs) are very rare relative to the Bobo numbers (A242679).

Exceptional Bobo numbers come in two varieties. Type-1 EBNs are given by the recurrence E(0)=1,E(1)=1,E(k)=(2*k-1)*(2*E(k-1)-1)+E(k-2) for k=3,5,7,... These are derived from the denominators of the odd-indexed convergents of the continued fraction expansion of (e-1)/2 = [0;1,6,10,14,18,...]. The Type-2 EBNs are derived from the Type-1 EBNs. They have the form n*m-(m-1)/2 where n is a Type-1 EBN and m>=3 is an odd integer. However, not every number of this form is an EBN.

References

• S. J. Kifowit, A. Mitchell, and S. Zandi, Exceptional Bobo Numbers, in preparation 2016

Links

• Steven J. Kifowit, Table of n, a(n) for n = 1..99
• 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, A242679 (Bobo numbers).