A139514 Denominators of an Egyptian fraction for Pi, using only prime numbers and allowing repetitions.

2, 2, 2, 2, 2, 2, 11, 23, 139, 90439, 33156439637, 87550414616253068989, 751473085670398285260591818545427587609, 9405222481347574254746223047204588161218024092399608112777273401749812628709

Offset

0,1

Links

Table of n, a(n) for n=0..13.

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

Cf. A139515-A139523.

Sequence in context: A129381 A319991 A323275 * A330955 A330956 A190617

Adjacent sequences: A139511 A139512 A139513 * A139515 A139516 A139517

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Apr 24 2008

Status

approved