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 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 (list; constant; graph; refs; listen; history; text; internal format)
 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 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: 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

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Last modified April 10 08:09 EDT 2021. Contains 342845 sequences. (Running on oeis4.)