

A172168


Decimal expansion of Sum 1/q, where q is any prime of the form m^2 + 1.


2



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

0,1


COMMENTS

The sum is trivially convergent because each term is less than the corresponding term of Sum_{j>=1} 1/(j^2) = (Pi^2)/6.
Eight significant digits of this constant are mentioned in A083844, which gives the number of primes of the form m^2 + 1 < 10^n.


LINKS

Table of n, a(n) for n=0..18.
G. L. Honaker Jr. and C. Caldwell, 0.81459657, Prime Curios!.
Marek Wolf, Search for primes of the form m^2+1, arXiv:0803.1456 [math.NT], 20082010, pp. 68.


FORMULA

Sum_{q in {primes of form m^2 + 1}} 1/q = Sum_{j>=1} 1/A002496(j) = 1/2 + 1/5 + 1/17 + 1/37 + 1/101 + ...


EXAMPLE

0.8145965717029728452...


CROSSREFS

Cf. A002496, A005597.
Sequence in context: A019981 A194281 A117038 * A321095 A021555 A298523
Adjacent sequences: A172165 A172166 A172167 * A172169 A172170 A172171


KEYWORD

nonn,cons,more


AUTHOR

Jonathan Vos Post, Jan 28 2010


EXTENSIONS

Leading zero removed and offset adjusted by R. J. Mathar, Jan 30 2010
Corrected and extended by Robert Gerbicz, Mar 13 2010
Name improved by T. D. Noe, Mar 29 2010


STATUS

approved



