A277750 Denominators of rationals R_n associated with an analog of Stern's diatomic sequence for Z[sqrt(2)].

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, 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, 13, 5, 17, 12, 7, 9, 11, 2, 9, 7, 5, 8, 11, 3, 7, 4, 1, 5, 9, 4, 15, 11, 7, 10

Offset: 1

Author

N. J. A. Sloane, Nov 08 2016

Keywords

• nonn
• frac

Examples

			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, ...
		

Links

• Gheorghe Coserea, Table of n, a(n) for n = 1..54321
• Florin P. Boca, Christopher Linden, On Minkowski type question mark functions associated with even or odd continued fractions, arXiv:1705.01238 [math.DS], 2017. See p. 10.
• S. Northshield, An Analogue of Stern's Sequence for Z[sqrt(2)], Journal of Integer Sequences, 18 (2015), #15.11.6.
• Lionel Ponton, Two trees enumerating the positive rationals, arXiv:1707.02366 [math.NT], 2017. See tree p. 4.
• Lionel Ponton, Two trees enumerating the positive rationals, Integers, Electronic Journal of Combinatorial Number Theory 18A (2018), #A17.
• Lukas Spiegelhofer, A Digit Reversal Property for an Analogue of Stern's Sequence, Journal of Integer Sequences, Vol. 20 (2017), #17.10.8.

Crossrefs

Cf. A002487 (Stern's diatomic sequence), A277749 (numerators).

Programs

Mathematica

R[1] = 2; R[n_] := R[n] = 4 IntegerExponent[n, 3] + 2 - 2/R[n-1];
Table[R[n] // Denominator, {n, 1, 100}] (* Jean-François Alcover, Sep 03 2018, after Gheorghe Coserea *)

PARI

seq(N) = {
  my(v = vector(N)); v[1] = 2;
  for (n = 2, N, v[n] = 4*valuation(n,3) + 2 - 2 / v[n-1]);
  return(v);
};
apply(denominator, seq(88))

Formula

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

Extensions

More terms from Gheorghe Coserea, Nov 11 2016