A002357 Denominators of convergents to cube root of 5.

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

Author

N. J. A. Sloane

Keywords

• nonn
• frac

Examples

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

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).

Crossrefs

Cf. A002358 (numerators), A005481.

Programs

PARI

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

Extensions

More terms from Herman P. Robinson

Offset changed by Andrew Howroyd, Jul 04 2024