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A092267 Values 2m_0+1 = 1, 2m_1, 2m_2+1, ... associated with divergent series T shown below.

%I A092267 #6 Mar 31 2012 10:29:04
%S A092267 1,454,45891,547208496,3013267310449,1961694770407970734,
%T A092267 589785633779065944213245,20963601300674244910397534828794,
%U A092267 344117353602393170461608383214200982125
%N A092267 Values 2m_0+1 = 1, 2m_1, 2m_2+1, ... associated with divergent series T shown below.
%C A092267 T = 1
%C A092267 - (1/2 + 1/4 + 1/6 + ... + 1/(2m_1))
%C A092267 + (1/3 + 1/5 + 1/7 + ... + 1/(2m_2+1))
%C A092267 - (1/(2m_1+2) + 1/(2m_1+4) + ... + 1/(2m_3)
%C A092267 + (1/(2m_2+3) + 1/(2m_2+5) + ... + 1/(2m_4+1))
%C A092267 - (1/(2m_3+2) + 1/(2m_3+4) + ... + 1/(2m_5)
%C A092267 + (1/(2m_4+3) + 1/(2m_4+5) + ... + 1/(2m_6+1))
%C A092267 - ...
%C A092267 where the partial sums of the terms from 1 through the end of rows 0, 1, ... are respectively 1, just < -2, just > 3, just < -4, just > 5, etc.
%C A092267 Every positive number appears exactly once as a denominator in T.
%C A092267 The series T is a divergent rearrangement of the conditionally convergent series Sum_{ j>=1} (-1)^j/j which has the entire real number system as its set of limit points.
%D A092267 B. R. Gelbaum and J. M. H. Olmsted, Counterexamples in Analysis, Holden-Day, San Francisco, 1964; see p. 55.
%e A092267 1 - (1/2 + 1/4 + 1/6 + ... + 1/454) = -2.002183354..., which is just less than -2; so a(1) = 2m_1 = 454.
%e A092267 1 - (1/2 + 1/4 + 1/6 + ... + 1/454) + (1/3 + 1/5 + ... + 1/45891) = 3.000021113057..., which is just greater than 3; so a(1) = 2m_2 + 1 = 45891.
%Y A092267 Cf. A092324 (essentially the same), A002387, A056053, A092318, A092317, A092315.
%Y A092267 Cf. A092273.
%K A092267 nonn,nice
%O A092267 0,2
%A A092267 _N. J. A. Sloane_, Feb 16 2004
%E A092267 a(2) and a(3) from _Hugo Pfoertner_, Feb 17 2004
%E A092267 a(4) onwards from _Hans Havermann_, Feb 18 2004