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 A247858 Decimal expansion of the value of the continued fraction [0; 2, 5, 17, 17, 37, 41, 97, 97, ...], generated with primes of the form a^2 + b^4. 3

%I

%S 4,5,5,0,2,4,8,1,6,4,9,0,1,7,0,0,2,2,3,6,9,0,5,2,8,0,8,2,7,9,7,4,4,8,

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

%U 6,0,8,5,0,1,0,7,1,8,6,3,1,4,3,6,3,1,0,6,6,7,6,9,7,5,4,6,0,4,5,1,9,9,2

%N Decimal expansion of the value of the continued fraction [0; 2, 5, 17, 17, 37, 41, 97, 97, ...], generated with primes of the form a^2 + b^4.

%H John Friedlander and Henryk Iwaniec, <a href="http://www.pnas.org/cgi/content/full/94/4/1054">Using a parity-sensitive sieve to count prime values of a polynomial</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Friedlander%E2%80%93Iwaniec_theorem">Friedlander-Iwaniec theorem</a>

%H Marek Wolf, <a href="http://arxiv.org/abs/1003.4015">Continued fractions constructed from prime numbers</a>, arxiv.org/abs/1003.4015, pp. 8-9.

%e 1/(2 + 1/(5 + 1/(17 + 1/(17 + 1/(37 + 1/(41 + 1/(97 + 1/(97 + ...))))))))

%e 0.45502481649017002236905280827974482410575554890507644...

%t max = 1000; r = Reap[Do[n = a^2 + b^4; If[n <= max && PrimeQ[n], Sow[n]], {a, Sqrt[max]}, {b, max^(1/4)}]][[2, 1]]; u = Union[r, SameTest -> (False&)] ; RealDigits[FromContinuedFraction[Join[{0}, u]], 10, 103] // First

%Y Cf. A028916, A243340, A247857.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Sep 25 2014

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Last modified October 18 04:46 EDT 2019. Contains 328145 sequences. (Running on oeis4.)