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A002351
Denominators of convergents to cube root of 2.
(Formerly M2380 N0945)
5
1, 3, 4, 23, 27, 50, 227, 277, 504, 4309, 4813, 71691, 76504, 836731, 1749966, 2586697, 12096754, 147747745, 307592244, 1070524477, 2448641198, 3519165675, 13006138223, 55543718567, 68549856790, 124093575357, 316737007504
OFFSET
0,2
REFERENCES
D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 67.
P. Seeling, Verwandlung der irrationalen Groesse ... in einen Kettenbruch, Archiv. Math. Phys., 46 (1866), 80-120.
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
E. Bombieri and A. J. van der Poorten, Continued fractions of algebraic numbers, In: Bosma W., van der Poorten A. (eds) Computational Algebra and Number Theory. Mathematics and Its Applications, vol 325.
E. B. Burger, Diophantine Olympics and World Champions: Polynomials and Primes Down Under, Amer. Math. Monthly, 107 (Nov. 2000), 822-829.
MAPLE
Digits := 60: E := 2^(1/3); convert(evalf(E), confrac, 50, 'cvgts'): cvgts;
# Alternate:
N:= 100: # to get a(1) to a(N)
c[0] := 1: p[0] := 1: a[0] := 0: p[1] := 1: a[1] := 1:
for n from 1 to N do
c[n] := floor((-1)^(n)*3*p[n]^2/(a[n]*(p[n]^3-2*a[n]^3)) - a[n-1]/a[n]);
p[n+1] := c[n]*p[n] + p[n-1];
a[n+1] := c[n]*a[n] + a[n-1];
od:
seq(a[i], i=1..N); # Robert Israel, Oct 08 2017
MATHEMATICA
Denominator[Convergents[Surd[2, 3], 30]] (* Harvey P. Dale, Apr 02 2018 *)
CROSSREFS
Cf. A002352 (numerators), A002945.
Sequence in context: A163744 A221643 A042595 * A042035 A343402 A030980
KEYWORD
nonn,frac
EXTENSIONS
Offset changed by Andrew Howroyd, Jul 04 2024
STATUS
approved