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

%I A277603 #17 Apr 04 2018 10:45:15
%S A277603 36,9045,5195512,5311399545,8488859795196,25466579385587,
%T A277603 19542965851120621,58628897553361862,61250772004870841520,
%U A277603 183752316014612524559,250769086731739376780337,752307260195218130341010,1299515735021702625544976020,3898547205065107876634928059
%N A277603 Exceptional Bobo numbers: terms of A242679 that satisfy frac[e*A242679(n)]<(e-1)/2.
%C A277603 The exceptional Bobo numbers (EBNs) are very rare relative to the Bobo numbers (A242679).
%C A277603 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.
%D A277603 S. J. Kifowit, A. Mitchell, and S. Zandi, Exceptional Bobo Numbers, in preparation 2016
%H A277603 Steven J. Kifowit, <a href="/A277603/b277603.txt">Table of n, a(n) for n = 1..99</a>
%H A277603 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 A277603 D. T. Clancy and S. J. Kifowit, <a href="http://www.jstor.org/stable/10.4169/college.math.j.45.3.199">A closer look at Bobo's sequence</a>, College Math. J. 45 (2014), 199-206.
%H A277603 Steve Kifowit, <a href="http://stevekifowit.com/pubs/denver.pdf">Bobo Numbers, Bobbers, and Bears—Experiences</a>, Undergraduate Research, Preprint, 2016.
%Y A277603 Cf. A103762, A242679 (Bobo numbers).
%K A277603 nonn
%O A277603 1,1
%A A277603 _Steven J. Kifowit_, Oct 22 2016