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A078585
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Decimal expansion of Sum_{n>=0} 1/4^(2^n).
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12
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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
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OFFSET
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0,1
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LINKS
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Aubrey J. Kempner, On Transcendental Numbers, Transactions of the American Mathematical Society, volume 17, number 4, October 1916, pages 476-482.
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FORMULA
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Equals -Sum_{k>=1} mu(2*k)/(4^k - 1), where mu is the Möbius function (A008683). - Amiram Eldar, Jul 12 2020
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EXAMPLE
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0.316421509021893143708079737530525221703311375920552804341210903843055...
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MATHEMATICA
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RealDigits[ N[ Sum[1/4^(2^n), {n, 0, Infinity}], 110]][[1]]
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PROG
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(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
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CROSSREFS
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Continued fraction is given in A006464.
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KEYWORD
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AUTHOR
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STATUS
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approved
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