

A349232


Decimal expansion of lim_{x>oo} (1/x) * Sum_{s(k+1) <= x} (s(k+1)  s(k))^2, where s(k) = A005117(k) is the kth squarefree number.


1



2, 0, 4, 0, 7, 0, 9, 7, 7, 6, 5
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OFFSET

1,1


COMMENTS

Erdős (1951) proved the existence of this limit and Mossinghoff et al. (2021) calculated its first 11 decimal digits.
Let g(n) = A076259(n) be the sequence of gaps between squarefree numbers. The asymptotic mean of g is <g> = Pi^2/6 (A013661). The second raw moment of g is <g^2> = (P^2/6) * 2.0407097765... = 3.35683303..., the second central moment, or variance, of g is <g^2>  <g>^2 = 0.651024947... and the standard deviation is sqrt(<g^2>  <g>^2) = 0.8068611...


LINKS



EXAMPLE

2.0407097765...


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AUTHOR



STATUS

approved



