A002357 Denominators of convergents to cube root of 5. (Formerly M2692 N1078)

1, 1, 3, 7, 31, 100, 331, 431, 2486, 2917, 5403, 24529, 250693, 4286310, 4537003, 67804352, 72341355, 140145707, 427797039119, 427937184826, 855734223945, 1283671408771, 2139405632716, 3423077041487, 5562482674203, 14548042389893

Offset

0,3

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

Table of n, a(n) for n=0..25.

Example

1 + 1/(1 + 1/(2 + 1/(2 + 1/4))) = 53/31 so a(5) = 31.

Prog

(PARI) a(n)=if(n<1, 0, contfracpnqn(contfrac(5^(1/3), n))[2, 1])

Crossrefs

Cf. A002358 (numerators), A005481.

Sequence in context: A257924 A358341 A132153 * A173062 A373755 A306831

Adjacent sequences: A002354 A002355 A002356 * A002358 A002359 A002360

Keyword

nonn,frac

Author

N. J. A. Sloane

Extensions

More terms from Herman P. Robinson

Offset changed by Andrew Howroyd, Jul 04 2024

Status

approved