cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A071353 First term of the continued fraction expansion of (3/2)^n.

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%I A071353 #21 Apr 21 2019 09:56:17
%S A071353 2,4,2,16,1,2,11,1,2,1,2,1,1,1,1,1,3,1,1,3,1,1,1,8,5,1,7,1,25,16,1,1,
%T A071353 1,1,1,2,1,1,1,3,2,1,1,1,3,1,1,2,7,4,3,2,4,1,3,1,3,1,1,1,2,10,1,2,4,1,
%U A071353 4,2,1,3,2,14,9,6,1,11,1,1,2,1,1,2,6,1,12,1,1,2,1,2,19,12,8,1,89,59,1,3
%N A071353 First term of the continued fraction expansion of (3/2)^n.
%C A071353 If uniformly distributed, then the average of the reciprocal terms of this sequence is 1/2.
%C A071353 "Pisot and Vijayaraghavan proved that (3/2)^n has infinitely many accumulation points, i.e. infinitely many convergent subsequences with distinct limits. The sequence is believed to be uniformly distributed, but no one has even proved that it is dense in [0,1]." - S. R. Finch.
%D A071353 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 192-199.
%H A071353 G. C. Greubel, <a href="/A071353/b071353.txt">Table of n, a(n) for n = 1..1000</a>
%H A071353 Steven R. Finch, <a href="/FinchPwrs32.html">Powers of 3/2 Modulo One</a> [From Steven Finch, Apr 20 2019]
%H A071353 Steven R. Finch, <a href="/FinchWaring.html">Non-Ideal Waring's Problem</a> [From Steven Finch, Apr 20 2019]
%H A071353 Jeff Lagarias, <a href="http://www.cecm.sfu.ca/organics/papers/lagarias/index.html">3x+1 Problem</a>
%H A071353 C. Pisot, <a href="http://www.numdam.org/item?id=ASNSP_1938_2_7_3-4_205_0">La répartition modulo 1 et les nombres algébriques</a>, Ann. Scuola Norm. Sup. Pisa, 7 (1938), 205-248.
%H A071353 T. Vijayaraghavan, <a href="https://doi.org/10.1112/jlms/s1-15.2.159">On the fractional parts of the powers of a number (I)</a>, J. London Math. Soc. 15 (1940) 159-160.
%F A071353 a(n) = floor(1/frac((3/2)^n)).
%e A071353 a(7) = 11 since floor(1/frac(3^7/2^7)) = floor(1/.0859375) = 11.
%t A071353 Table[Floor[1/FractionalPart[(3/2)^n]], {n, 1, 100}] (* _G. C. Greubel_, Apr 18 2017 *)
%o A071353 (PARI) a(n) = contfrac((3/2)^n)[2] \\ _Michel Marcus_, Aug 01 2013
%Y A071353 Cf. A055500, A071291.
%K A071353 easy,nonn
%O A071353 1,1
%A A071353 _Paul D. Hanna_, Jun 10 2002