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 A092267 Values 2m_0+1 = 1, 2m_1, 2m_2+1, ... associated with divergent series T shown below. 2
 1, 454, 45891, 547208496, 3013267310449, 1961694770407970734, 589785633779065944213245, 20963601300674244910397534828794, 344117353602393170461608383214200982125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS T = 1 - (1/2 + 1/4 + 1/6 + ... + 1/(2m_1)) + (1/3 + 1/5 + 1/7 + ... + 1/(2m_2+1)) - (1/(2m_1+2) + 1/(2m_1+4) + ... + 1/(2m_3) + (1/(2m_2+3) + 1/(2m_2+5) + ... + 1/(2m_4+1)) - (1/(2m_3+2) + 1/(2m_3+4) + ... + 1/(2m_5) + (1/(2m_4+3) + 1/(2m_4+5) + ... + 1/(2m_6+1)) - ... 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. Every positive number appears exactly once as a denominator in T. 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. REFERENCES B. R. Gelbaum and J. M. H. Olmsted, Counterexamples in Analysis, Holden-Day, San Francisco, 1964; see p. 55. LINKS EXAMPLE 1 - (1/2 + 1/4 + 1/6 + ... + 1/454) = -2.002183354..., which is just less than -2; so a(1) = 2m_1 = 454. 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. CROSSREFS Cf. A092324 (essentially the same), A002387, A056053, A092318, A092317, A092315. Cf. A092273. Sequence in context: A234771 A297658 A219006 * A232758 A284430 A206338 Adjacent sequences:  A092264 A092265 A092266 * A092268 A092269 A092270 KEYWORD nonn,nice AUTHOR N. J. A. Sloane, Feb 16 2004 EXTENSIONS a(2) and a(3) from Hugo Pfoertner, Feb 17 2004 a(4) onwards from Hans Havermann, Feb 18 2004 STATUS approved

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Last modified May 10 00:50 EDT 2021. Contains 343747 sequences. (Running on oeis4.)