

A372947


Decimal expansion of Sum_{k >= 0} (10^5*A196563(k)  A196564(k)/10^5)/10^k.


1



1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9, 0, 9
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OFFSET

6,12


COMMENTS

Bradshaw and Vignat (2023, p. 12) show that, in general, for p >= 1 Sum_{k >= 0} c_p(k)/10^(p*k) can be approximated by [1[0]_{p1}]_{10}1/1[0]_{p1}1[0]_{4*p} with an error on the order of 10^(105*p), where c_p(k) = 10^(p*5)*A196563(k)  A196564(k)/10^(p*5) and [x]_{r} denotes r copies of x.
E.g., for p = 2 we have that Sum_{k >= 0} c_2(k)/10^(2*k) = Sum_{k >= 0} (10^(2*5)*A196563(k)  A196564(k)/10^(2*5))/10^(2*k) can be approximated by 101010101010101010101/10100000000.


LINKS



FORMULA

Approximately 11111111111/110000, correct to 109 digits: see Entry 5 in Bradshaw and Vignat (2023), pp. 1 and 1012.


EXAMPLE

101010.10100909090909090909090909090909090909090909090909090...


MATHEMATICA

First[RealDigits[Sum[(10^5*Count[IntegerDigits[k], _?EvenQ]  Count[IntegerDigits[k], _?OddQ]/10^5)/10^k, {k, 0, 100}], 10, 100]]


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



