A002351 Denominators of convergents to cube root of 2. (Formerly M2380 N0945)

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

1,2

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

Robert Israel, Table of n, a(n) for n = 1..1976

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, A002945.

Sequence in context: A163744 A221643 A042595 * A042035 A343402 A030980

Adjacent sequences: A002348 A002349 A002350 * A002352 A002353 A002354

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved