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 A002486 Apart from two leading terms (which are present by convention), denominators of convergents to Pi (A002485 and A046947 give numerators). (Formerly M4456 N1886) 26
 1, 0, 1, 7, 106, 113, 33102, 33215, 66317, 99532, 265381, 364913, 1360120, 1725033, 25510582, 52746197, 78256779, 131002976, 340262731, 811528438, 1963319607, 4738167652, 6701487259, 567663097408, 1142027682075, 1709690779483, 2851718461558, 44485467702853 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Disregarding first two terms, integer diameters of circles beginning with 1 and a(n+1) is the smallest integer diameter with corresponding circumference nearer an integer than is the circumference of the circle with diameter a(n). See PARI program. - Rick L. Shepherd, Oct 06 2007 a(n+1) = numerator of fraction obtained from truncated continued fraction expansion of 1/Pi to n terms. - Artur Jasinski, Mar 25 2008 REFERENCES P. Beckmann, A History of Pi. Golem Press, Boulder, CO, 2nd ed., 1971, p. 171 (but beware errors). CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 88. K. H. Rosen et al., eds., Handbook of Discrete and Combinatorial Mathematics, CRC Press, 2000; p. 293. 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 T. D. Noe, Table of n, a(n) for n=0..201 E. B. Burger, Diophantine Olympics and World Champions: Polynomials and Primes Down Under, Amer. Math. Monthly, 107 (Nov. 2000), 822-829. Marc Daumas, Des implantations differentes ..., see p. 8. P. Finsler, Über die Faktorenzerlegung natuerlicher Zahlen, Elemente der Mathematik, 2 (1947), 1-11, see p. 7. Henryk Fuks, Adam Adamandy Kochanski's approximations of pi: reconstruction of the algorithm, arXiv preprint arXiv:1111.1739, 2011. Math. Intelligencer, Vol. 34 (No. 4), 2012, pp. 40-45. G. P. Michon, Continued Fractions Eric Weisstein's World of Mathematics, Pi. Eric Weisstein's World of Mathematics, Pi Continued Fraction Eric Weisstein's World of Mathematics, Pi Approximations EXAMPLE The convergents are 3, 22/7, 333/106, 355/113, 103993/33102, ... MAPLE Digits := 60: E := Pi; convert(evalf(E), confrac, 50, 'cvgts'): cvgts; with(numtheory):cf := cfrac (Pi, 100): seq(nthdenom (cf, i), i=-2..28 ); # Zerinvary Lajos, Feb 07 2007 MATHEMATICA b = {1}; Do[c = Numerator[FromContinuedFraction[ContinuedFraction[1/Pi, n]]]; AppendTo[b, c], {n, 1, 30}]; b (* Artur Jasinski, Mar 25 2008 *) Join[{1, 0}, Denominator[Convergents[Pi, 30]]] (* Harvey P. Dale, Sep 13 2013 *) PROG (PARI) /* Program calculates a(n) (slowly) without continued fraction function */ {c=frac(Pi); print1("1, 0, 1, "); for(diam=2, 500000000, cm=diam*Pi; cmin=min(cm-floor(cm), ceil(cm)-cm); \ if(cmin

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Last modified December 21 23:06 EST 2014. Contains 252326 sequences.