A156618
Denominators of Egyptian fraction for Pi-3 whose partial sums are the convergents.
Original entry on oeis.org
7, -742, 11978, -3740526, 1099482930, -2202719155, 6600663644, -26413901692, 96840976853, -496325469560, 2346251883960, -44006595799206, 1345586183756654, -4127747481719463, 10251870941174304
Offset: 0
3+1/a(0)=22/7
3+1/a(0)+1/a(1)=333/106
3+1/a(0)+1/a(1)+1/a(2)=355/113
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c0=3; for (k=2,30,m=contfracpnqn(contfrac(Pi,k));c1=m[1,1]/m[2,1];print1(1/(c1-c0),", ");c0=c1;)
A001467
Denominators of an expansion for Pi.
Original entry on oeis.org
1, 1, 1, 7, -791, -3748629, 151648960887729, -1323497544567561138595307148089, 41444465282455711991644958522615049159671653083333293470875123
Offset: 0
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...
- 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).
- 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
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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
A052385
a(n)*10^n are the denominators of the greedy alternating Egyptian fraction expansion of Pi - 3 of the form Sum_{n>=0} (-1)^n / (a(n)*10^n).
Original entry on oeis.org
7, 79, 7498, 5830114, 8652011824287, 13597204960705459608723126, 34810495772672927583903155370200945603822050731477, 1443540369391032855921234984363709782471552979298036142515612532020988429757781997263178546460721652
Offset: 0
Boris Gourevitch (sai1042(AT)ensai.fr), Mar 10 2000
Pi = 3 + 1/7 - 1/(10 * 79) + 1/(10^2 * 7498) - 1/(10^3 * 5830114) + ...
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s={}; x = Pi - 3; Do[a = Floor[1/((-10)^k * x)]; AppendTo[s, a]; x-=1/((-10)^k*a), {k, 0, 7}]; s (* Amiram Eldar, Jan 23 2019 *)
A304798
Denominators of sign-alternating Egyptian fraction expansion for 1/phi (=(sqrt(5)-1)/2).
Original entry on oeis.org
1, 2, 8, 143, 37042, 1563518960, 6534294597508602915, 365905726475037211039550490160754059749, 191234231522546096496793980270535044877607924567064996105428722406747743518730
Offset: 0
a(0)=1 since 1/phi is between 1/1 and 1/2 and 1/1 > 1/phi; i.e., floor(1/(1/phi)) = 1.
a(1)=2 since floor(1/(1/a(0) - 1/phi)) = 2.
a(2)=8 since floor(1/(1/phi - (1/a(0)-1/a(1)))) = 8, and so on.
Showing 1-4 of 4 results.
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