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%I #3 Aug 24 2012 10:50:01
%S 2,2,2,2,2,2,11,23,139,90439,33156439637,87550414616253068989,
%T 751473085670398285260591818545427587609,
%U 9405222481347574254746223047204588161218024092399608112777273401749812628709
%N Denominators of an Egyptian fraction for Pi, using only prime numbers and allowing repetitions.
%e 1/2+1/2+1/2+1/2+1/2+1/2 = 3 (integer part of Pi)
%e 3+1/11+1/23+1/139+1/90439 gives an approximation which is good to 10 decimal digits.
%e Adding the other fractions we reach a good approximation to 19, 38, 75, 149, 296, 591 decimal digits.
%p P:=proc(n) local a,i; a:=evalf(Pi-3,100); for i from 1 by 1 to 6 do print(2); od; 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. A139515-A139523.
%K easy,nonn
%O 0,1
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Apr 24 2008
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