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%I #8 Mar 28 2015 14:57:30
%S 8,62,454,3348,24734,182760,1350428,9978382,73730824,544801200,
%T 4025566630,29745137662,219788490858,1624029488844,12000044999386,
%U 88669005690160,655180257281000,4841163675961122,35771629985782052
%N a(n) = smallest even number 2m such that value of odd harmonic series Sum_{j=0..m} 1/(2j) is > n.
%C Numbers 2*m such that floor(f(m))=floor(f(m-1)) where f(m)= Sum_{j=1..m} ((2*j-1)/(2*j)). Examples: floor(f(1))=floor(1/2)=0; floor(f(2))=floor(1/2+2/3)=floor(1,25)=1, then 2*2=4 is not in the sequence; floor(f(3))=floor((1/2+3/4+4/5)=floor(2,083..)=2, then 2*3=6 is not in the sequence; floor((f(4))=floor(1/2+3/4+5/6+7/8)=floor(2,958..)=2, then 2*4=8 is the first term of the sequence. - Philippe Lallouet (philip.lallouet(AT)wanadoo.fr), Aug 15 2007
%D Calvin C. Clawson, Mathematical Mysteries, The Beauty and Magic of Numbers, Plenum Press, NY and London, 1996, page 64.
%F a(n) = 2*A002387(2n).
%F The next term is approximately the previous term * e^2.
%t s = 0; k = 2; Do[ While[s = N[s + 1/k, 24]; s <= n, k += 2]; Print[k]; k += 2, {n, 1, 12}]
%t (* or assuming that the Mathematica coding in A002387 is correct then *)
%t b[n_] := Module[{k = Floor[2a[2n]]}, If[ EvenQ[k], k, k + 1]]; Table[ b[n], {n, 19}] (* _Robert G. Wilson v_, Apr 17 2004 *)
%Y Cf. A002387, A056053, A091463, A091464, A091465.
%Y Cf. A056054.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Jul 25 2000 and Jan 11 2004
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