A080032 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".

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, 27, 38, 40, 42, 31, 44, 46, 48, 35, 50, 52, 54, 39, 56, 58, 60, 43, 62, 64, 66, 47, 68, 70, 72, 51, 74, 76, 78, 55, 80, 82, 84, 59, 86, 88, 90, 63, 92, 94, 96, 67, 98, 100, 102, 71, 104

Offset

0,2

Comments

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

If "even" in the definition is replaced by "prime", we get A121053. - N. J. A. Sloane, Dec 14 2024

Links

Michael De Vlieger, Table of n, a(n) for n = 0..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).

Formula

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.

From Chai Wah Wu, Apr 13 2024: (Start)

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

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)

Mathematica

CoefficientList[Series[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), {x, 0, 120}], x] (* Michael De Vlieger, Dec 17 2024 *)

Crossrefs

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

Sequence in context: A128860 A019680 A249144 * A297121 A105357 A346246

Adjacent sequences: A080029 A080030 A080031 * A080033 A080034 A080035

Keyword

easy,nonn

Author

N. J. A. Sloane, Mar 14 2003

Extensions

More terms from Matthew Vandermast, Mar 21 2003

Status

approved