login
A139514
Denominators of an Egyptian fraction for Pi, using only prime numbers and allowing repetitions.
9
2, 2, 2, 2, 2, 2, 11, 23, 139, 90439, 33156439637, 87550414616253068989, 751473085670398285260591818545427587609, 9405222481347574254746223047204588161218024092399608112777273401749812628709
OFFSET
0,1
EXAMPLE
1/2+1/2+1/2+1/2+1/2+1/2 = 3 (integer part of Pi)
3+1/11+1/23+1/139+1/90439 gives an approximation which is good to 10 decimal digits.
Adding the other fractions we reach a good approximation to 19, 38, 75, 149, 296, 591 decimal digits.
MAPLE
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);
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved