A160386 Decimal expansion of Sum_{n>=0}(-1)^n/3^(2^n).

2, 3, 4, 4, 1, 5, 5, 0, 8, 6, 7, 4, 8, 6, 4, 6, 1, 4, 4, 1, 3, 4, 1, 5, 4, 7, 4, 3, 4, 5, 6, 0, 4, 5, 9, 7, 6, 1, 4, 7, 2, 4, 5, 6, 3, 9, 0, 6, 6, 9, 3, 0, 2, 7, 6, 7, 9, 4, 2, 7, 7, 3, 7, 0, 9, 8, 3, 8, 1, 4, 3, 1, 5, 1, 3, 7, 5, 8, 5, 3, 5, 3, 1, 0, 3, 7, 5, 6, 5, 6, 5, 9, 8, 4, 9, 7, 6, 5, 9, 8, 4, 4, 0, 6, 4

Offset: 0

Author

Harry J. Smith, May 12 2009

Keywords

• nonn
• cons

Comments

This sum is among forms which Kempner showed are transcendental. - Kevin Ryde, Sep 16 2019

Examples

			0.234415508674864614413415474345604597614724563906693027679427737098381...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000
• Aubrey J. Kempner, On Transcendental Numbers, Transactions of the American Mathematical Society, Vol. 17, No. 4 (October 1916), pp. 476-482.
• Index entries for transcendental numbers.

Crossrefs

Cf. A006467 (continued fraction), A030300 (ternary expansion).

Programs

Mathematica

RealDigits[N[Sum[(-1)^n/3^(2^n), {n, 0, Infinity}], 120]][[1]] (* Amiram Eldar, Jun 11 2023 *)

PARI

{ default(realprecision, 20080); x=10*suminf(n=0, (-1)^n/3^(2^n)); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b160386.txt", n, " ", d)); }