A080032 - OEIS

%I #24 Dec 14 2024 22:03:37

%S 0,2,4,1,6,7,8,10,12,11,14,16,18,15,20,22,24,19,26,28,30,23,32,34,36,

%T 27,38,40,42,31,44,46,48,35,50,52,54,39,56,58,60,43,62,64,66,47,68,70,

%U 72,51,74,76,78,55,80,82,84,59,86,88,90,63,92,94,96,67,98,100,102,71,104

%N 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 even".

%C The same sequence, but without the initial 0, obeys the rule: "The concatenation of a(n) and a(a(n)) is even". Example: "2" and the 2nd term, concatenated, is 24; "4" and the 4th term, concatenated, is 46; "1" and the 1st term, concatenated, is 12; etc. - _Eric Angelini_, Feb 22 2017

%C If "even" in the definition is replaced by "prime", we get A121053. - _N. J. A. Sloane_, Dec 14 2024

%H B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Cloitre/cloitre2.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.

%H B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://arXiv.org/abs/math.NT/0305308">Numerical analogues of Aronson's sequence</a>, arXiv:math/0305308 [math.NT], 2003.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).

%F For n >= 4 a(n) is given by: a(4m)=6m, a(4m+1)=4m+3, a(4m+2)=6m+2, a(4m+3)=6m+4.

%F From _Chai Wah Wu_, Apr 13 2024: (Start)

%F a(n) = 2*a(n-4) - a(n-8) for n > 11.

%F G.f.: x*(-3*x^10 + 2*x^9 - x^8 + 8*x^6 + 3*x^4 + 6*x^3 + x^2 + 4*x + 2)/(x^8 - 2*x^4 + 1). (End)

%Y Cf. A079000, A080029, A080030, A121053. Equals A079313 - 1.

%K easy,nonn,changed

%O 0,2

%A _N. J. A. Sloane_, Mar 14 2003

%E More terms from _Matthew Vandermast_, Mar 21 2003