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Denominators of convergents to cube root of 5.
(Formerly M2692 N1078)
2

%I M2692 N1078 #24 Jul 04 2024 20:06:56

%S 1,1,3,7,31,100,331,431,2486,2917,5403,24529,250693,4286310,4537003,

%T 67804352,72341355,140145707,427797039119,427937184826,855734223945,

%U 1283671408771,2139405632716,3423077041487,5562482674203,14548042389893

%N Denominators of convergents to cube root of 5.

%D D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 67.

%D P. Seeling, Verwandlung der irrationalen Groesse ... in einen Kettenbruch, Archiv. Math. Phys., 46 (1866), 80-120.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

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

%Y Cf. A002358 (numerators), A005481.

%K nonn,frac

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Herman P. Robinson_

%E Offset changed by _Andrew Howroyd_, Jul 04 2024