A001467 Denominators of an expansion for Pi.

1, 1, 1, 7, -791, -3748629, 151648960887729, -1323497544567561138595307148089, 41444465282455711991644958522615049159671653083333293470875123

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• frac

Examples

			a(4) = -791 since Pi - (1/1) - (1/1) - (1/1) - (1/7) = -0.001264489... is closer to 1/(-791) = -0.001264222... than to 1/(-790) = -0.0012658228...
		

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Mohammad K. Azarian, An Expression for Pi, Problem #870, College Mathematics Journal, Vol. 39, No. 1, January 2008, p. 66. Solution appeared in Vol. 40, No. 1, January 2009, pp. 62-64.
• H. E. Salzer, The approximation of numbers as sums of reciprocals, Amer. Math. Monthly, 54 (1947), 135-142.
• J. W. Wrench, Jr., Letter to N. J. A. Sloane, Mar 27 1974
• Index entries for sequences related to the number Pi

Crossrefs

Cf. A001466, A014013, A073422.

Programs

PARI

x=Pi; for(k=0,8,if(x<1,d=round(1/x),d=1); x=x-1/d; print(d,", ")) \\ Jaume Oliver Lafont, Feb 21 2009

Formula

Numerators are 1.

Extensions

Edited by Henry Bottomley, Jul 30 2002