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%I #46 Sep 03 2018 03:38:25
%S 1,1,1,2,3,1,3,2,1,3,5,2,7,5,3,4,5,1,5,4,3,5,7,2,5,3,1,4,7,3,11,8,5,7,
%T 9,2,11,9,7,12,17,5,13,8,3,7,11,4,13,9,5,6,7,1,7,6,5,9,13,4,11,7,3,8,
%U 13,5,17,12,7,9,11,2,9,7,5,8,11,3,7,4,1,5,9,4,15,11,7,10
%N Denominators of rationals R_n associated with an analog of Stern's diatomic sequence for Z[sqrt(2)].
%H Gheorghe Coserea, <a href="/A277750/b277750.txt">Table of n, a(n) for n = 1..54321</a>
%H Florin P. Boca, Christopher Linden, <a href="https://arxiv.org/abs/1705.01238">On Minkowski type question mark functions associated with even or odd continued fractions</a>, arXiv:1705.01238 [math.DS], 2017. See p. 10.
%H S. Northshield, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Northshield/north4.html">An Analogue of Stern's Sequence for Z[sqrt(2)]</a>, Journal of Integer Sequences, 18 (2015), #15.11.6.
%H Lionel Ponton, <a href="https://arxiv.org/abs/1707.02366">Two trees enumerating the positive rationals</a>, arXiv:1707.02366 [math.NT], 2017. See tree p. 4.
%H Lionel Ponton, <a href="http://math.colgate.edu/~integers/sjs17/sjs17.Abstract.html">Two trees enumerating the positive rationals</a>, Integers, Electronic Journal of Combinatorial Number Theory 18A (2018), #A17.
%H Lukas Spiegelhofer, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Spiegelhofer/spieg2.html">A Digit Reversal Property for an Analogue of Stern's Sequence</a>, Journal of Integer Sequences, Vol. 20 (2017), #17.10.8.
%F a(n) = denominator(R(n)), where R(n) = 4 * A007949(n) + 2 - 2/R(n-1), with R(1) = 2. - _Gheorghe Coserea_, Nov 11 2016
%e 2, 1, 4, 3/2, 2/3, 3, 4/3, 1/2, 6, 5/3, 4/5, 7/2, 10/7, 3/5, 8/3, 5/4, 2/5, 5, 8/5, 3/4, ...
%t R[1] = 2; R[n_] := R[n] = 4 IntegerExponent[n, 3] + 2 - 2/R[n-1];
%t Table[R[n] // Denominator, {n, 1, 100}] (* Jean-François Alcover, Sep 03 2018, after Gheorghe Coserea *)
%o (PARI)
%o seq(N) = {
%o my(v = vector(N)); v[1] = 2;
%o for (n = 2, N, v[n] = 4*valuation(n,3) + 2 - 2 / v[n-1]);
%o return(v);
%o };
%o apply(denominator, seq(88))
%Y Cf. A002487 (Stern's diatomic sequence), A277749 (numerators).
%K nonn,frac
%O 1,4
%A _N. J. A. Sloane_, Nov 08 2016
%E More terms from _Gheorghe Coserea_, Nov 11 2016
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