

A277603


Exceptional Bobo numbers: terms of A242679 that satisfy frac[e*A242679(n)]<(e1)/2.


2



36, 9045, 5195512, 5311399545, 8488859795196, 25466579385587, 19542965851120621, 58628897553361862, 61250772004870841520, 183752316014612524559, 250769086731739376780337, 752307260195218130341010, 1299515735021702625544976020, 3898547205065107876634928059
(list;
graph;
refs;
listen;
history;
text;
internal format)



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. Type1 EBNs are given by the recurrence E(0)=1,E(1)=1,E(k)=(2*k1)*(2*E(k1)1)+E(k2) for k=3,5,7,... These are derived from the denominators of the oddindexed convergents of the continued fraction expansion of (e1)/2 = [0;1,6,10,14,18,...]. The Type2 EBNs are derived from the Type1 EBNs. They have the form n*m(m1)/2 where n is a Type1 EBN and m>=3 is an odd integer. However, not every number of this form is an EBN.


REFERENCES

Steve Kifowit, Bobo Numbers, Bobbers, and Bearsâ€”Experiences in Undergraduate Research, Preprint, 2016; http://stevekifowit.com/pubs/denver.pdf
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), 308310.
D. T. Clancy and S. J. Kifowit, A closer look at Bobo's sequence, College Math. J. 45 (2014), 199206.


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



