cp's OEIS Frontend

A277749 Numerators of rationals R_n associated with an analog of Stern's diatomic sequence for Z[sqrt(2)].

%I A277749 #54 Sep 03 2018 03:38:31
%S A277749 2,1,4,3,2,3,4,1,6,5,4,7,10,3,8,5,2,5,8,3,10,7,4,5,6,1,8,7,6,11,16,5,
%T A277749 14,9,4,11,18,7,24,17,10,13,16,3,14,11,8,13,18,5,12,7,2,7,12,5,18,13,
%U A277749 8,11,14,3,16,13,10,17,24,7,18,11,4,9,14,5,16,11,6,7,8,1,10,9,8,15,22,7,20,13
%N A277749 Numerators of rationals R_n associated with an analog of Stern's diatomic sequence for Z[sqrt(2)].
%C A277749 "At the end of Section 6, the sequences of numerators and denominators of R_n were considered. What do these sequences count? Further, is there some kind of combinatorial reciprocity [Beck] occurring here?" - [S. Northshield]
%H A277749 Gheorghe Coserea, <a href="/A277749/b277749.txt">Table of n, a(n) for n = 1..54321</a>
%H A277749 Matthias Beck, <a href="https://arxiv.org/abs/1201.2212">Combinatorial Reciprocity Theorems</a>, arXiv:1201.2212 [math.CO], 2012.
%H A277749 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 A277749 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 A277749 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 A277749 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 A277749 a(n) = numerator(R(n)), where R(n) = 4 * A007949(n) + 2 - 2/R(n-1), with R(1) = 2. - _Gheorghe Coserea_, Nov 11 2016
%e A277749 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 A277749 R[1] = 2; R[n_] := R[n] = 4 IntegerExponent[n, 3] + 2 - 2/R[n-1];
%t A277749 Table[R[n] // Numerator, {n, 1, 100}] (* _Jean-François Alcover_, Sep 03 2018, after _Gheorghe Coserea_ *)
%o A277749 (PARI)
%o A277749 seq(N) = {
%o A277749   my(v = vector(N)); v[1] = 2;
%o A277749   for (n = 2, N, v[n] = 4*valuation(n,3) + 2 - 2 / v[n-1]);
%o A277749   return(v);
%o A277749 };
%o A277749 apply(numerator, seq(88))  \\ _Gheorghe Coserea_, Nov 11 2016
%Y A277749 Cf. A002487 (Stern's diatomic sequence), A277750 (denominators).
%K A277749 nonn,frac
%O A277749 1,1
%A A277749 _N. J. A. Sloane_, Nov 08 2016
%E A277749 More terms from _Gheorghe Coserea_, Nov 11 2016