A172168 Decimal expansion of Sum 1/q, where q is any prime of the form m^2 + 1.

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

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], 2008-2010, pp. 6-8.

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: A194281 A117038 A365935 * A371874 A321095 A021555

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