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

1,1

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).

Sequence in context: A268553 A233171 A058466 * A141475 A233126 A201003

Adjacent sequences: A277600 A277601 A277602 * A277604 A277605 A277606

Keyword

nonn

Author

Steven J. Kifowit, Oct 22 2016

Status

approved