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

Author

Jonathan Vos Post, Jan 28 2010

Keywords

• nonn
• cons
• more

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.

Examples

			0.8145965717029728452...
		

Links

• 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.

Crossrefs

Cf. A002496, A005597.

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 + ...

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