A079313 a(n) is taken to be the smallest positive integer not already present which is consistent with the condition "n is a member of the sequence if and only if a(n) is odd".
1, 3, 5, 2, 7, 8, 9, 11, 13, 12, 15, 17, 19, 16, 21, 23, 25, 20, 27, 29, 31, 24, 33, 35, 37, 28, 39, 41, 43, 32, 45, 47, 49, 36, 51, 53, 55, 40, 57, 59, 61, 44, 63, 65, 67, 48, 69, 71, 73, 52, 75, 77, 79, 56, 81, 83, 85, 60, 87, 89, 91, 64, 93, 95, 97, 68, 99, 101, 103, 72, 105
Offset: 1
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
- Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
- Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).
Programs
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Mathematica
Rest@ CoefficientList[Series[x*(-3*x^11 + 2*x^10 - x^9 + 7*x^7 - x^6 + 2*x^5 + 5*x^4 + 2*x^3 + 5*x^2 + 3*x + 1)/(x^8 - 2*x^4 + 1), {x, 0, 120}], x] (* Michael De Vlieger, Dec 17 2024 *)
Formula
For n >= 5 a(n) is given by: a(4t-2) = 4t, a(4t-1) = 6t-3, a(4t) = 6t-1, a(4t+1) = 6t+1.
All odd numbers occur; the only even numbers which occur are 2 and the multiples of 4 excluding 4 itself.
From Chai Wah Wu, Apr 13 2024: (Start)
a(n) = 2*a(n-4) - a(n-8) for n > 12.
G.f.: x*(-3*x^11 + 2*x^10 - x^9 + 7*x^7 - x^6 + 2*x^5 + 5*x^4 + 2*x^3 + 5*x^2 + 3*x + 1)/(x^8 - 2*x^4 + 1). (End)
Extensions
More terms from Matthew Vandermast, Mar 20 2003
Comments