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Denominators of an Egyptian Fraction for sqrt(2), using only prime numbers and allowing repetitions.
2

%I #3 Aug 24 2012 10:50:01

%S 2,2,3,13,257,15131,83002267,1696274711037607,

%T 62384117997457733544603820483,

%U 36029882103194027595685829384642730184657157184554323517

%N Denominators of an Egyptian Fraction for sqrt(2), using only prime numbers and allowing repetitions.

%C Good approximation up to 799 decimal digits

%p P:=proc(n) local a,i; a:=evalf((sqrt(2))-1,100); print(2); print(2); for i from 1 by 1 to n do if 1/ithprime(i)<a then a:=a-1/ithprime(i); print(a); print(ithprime(i)); fi; od; end: P(100000);

%Y Cf. A139514-A139520, A139522, A139523.

%K easy,nonn,frac

%O 0,1

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Apr 28 2008