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A002357
Denominators of convergents to cube root of 5.
(Formerly M2692 N1078)
2
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).
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
KEYWORD
nonn,frac
EXTENSIONS
More terms from Herman P. Robinson
Offset changed by Andrew Howroyd, Jul 04 2024
STATUS
approved