0,2

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.

B. R. Gelbaum and J. M. H. Olmsted, Counterexamples in Analysis, Holden-Day, San Francisco, 1964; see p. 55.

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.

Cf. A092324 (essentially the same), A002387, A056053, A092318, A092317, A092315.

Cf. A092273.

Sequence in context: A116308 A081739 A076547 this_sequence A123563 A043475 A061544

Adjacent sequences: A092264 A092265 A092266 this_sequence A092268 A092269 A092270

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com), Feb 16 2004

a(2) and a(3) from Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 17 2004

a(4) onwards from Hans Havermann (pxp(AT)rogers.com), Feb 18 2004