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A275975 Decimal expansion of Sum_{k>=0}((-1)^k/2^(2^k)). 1
3, 0, 8, 6, 0, 9, 0, 0, 8, 5, 5, 6, 2, 3, 1, 8, 5, 6, 4, 0, 0, 3, 4, 0, 4, 7, 9, 7, 1, 8, 0, 2, 5, 2, 2, 1, 6, 9, 7, 4, 3, 3, 9, 0, 4, 1, 6, 6, 4, 4, 1, 3, 6, 6, 8, 0, 1, 3, 6, 7, 2, 2, 1, 1, 5, 6, 9, 4, 4, 3, 8, 5, 8, 0, 5, 4, 6, 1, 9, 7, 2, 2, 7, 6, 6, 2, 4, 8, 7, 5, 6, 4, 0, 8, 5, 3, 5, 0, 7, 0, 8, 6, 1, 6, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Except for the alternating signs, this constant is defined in a similar way to the Kempner-Mahler number A007404. It is related to the Jeffreys binary sequence A275973 somewhat like Kempner-Mahler number is related to the Fredholm-Rueppel sequence A036987.

Conjecture: Numbers of the type Sum_{k>=0}(x^(2^k)) with algebraic x and |x|<1 are known to be transcendental (Mahler 1930, Adamczewski 2013). It is likely that the alternating sign does not invalidate this property.

LINKS

Table of n, a(n) for n=0..104.

B. Adamczewski, The Many Faces of the Kempner Number, arXiv:1303.1685 [math.NT], 2013.

K. Mahler, Arithmetische Eigenschaften einer Klasse transzendental-transzendente Funktionen, Math. Z. 32 (1930), 545-585.

EXAMPLE

0.308609008556231856400340479718025221697433904166441366801367221...

PROG

(PARI) default(realprecision, 2100); suminf(k=0, (-1)^k*0.5^2^k)

CROSSREFS

Cf. A007404, A036987, A275973.

Sequence in context: A201577 A223854 A248424 * A201665 A137204 A021328

Adjacent sequences:  A275972 A275973 A275974 * A275976 A275977 A275978

KEYWORD

nonn,cons

AUTHOR

Stanislav Sykora, Aug 15 2016

STATUS

approved

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Last modified May 22 16:19 EDT 2017. Contains 286882 sequences.