A078585 Decimal expansion of Sum_{n>=0} 1/4^(2^n).
3, 1, 6, 4, 2, 1, 5, 0, 9, 0, 2, 1, 8, 9, 3, 1, 4, 3, 7, 0, 8, 0, 7, 9, 7, 3, 7, 5, 3, 0, 5, 2, 5, 2, 2, 1, 7, 0, 3, 3, 1, 1, 3, 7, 5, 9, 2, 0, 5, 5, 2, 8, 0, 4, 3, 4, 1, 2, 1, 0, 9, 0, 3, 8, 4, 3, 0, 5, 5, 6, 1, 4, 1, 9, 4, 5, 5, 5, 3, 0, 0, 0, 6, 0, 4, 8, 5, 3, 1, 3, 2, 4, 8, 3, 9, 7, 2, 6, 5, 6, 1, 7, 5, 5, 8
Offset: 0
Examples
0.316421509021893143708079737530525221703311375920552804341210903843055...
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, volume 17, number 4, October 1916, pages 476-482.
- Index entries for transcendental numbers
Crossrefs
Programs
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Mathematica
RealDigits[ N[ Sum[1/4^(2^n), {n, 0, Infinity}], 110]][[1]] -
PARI
{ default(realprecision, 20080); x=suminf(n=0, 1/4^(2^n)); x*=10; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b078585.txt", n, " ", d)); } \\ Harry J. Smith, May 11 2009
Formula
Equals -Sum_{k>=1} mu(2*k)/(4^k - 1), where mu is the Möbius function (A008683). - Amiram Eldar, Jul 12 2020
Equals A007404 - 1/2. - Kevin Ryde, Nov 11 2020