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

1,2

Comments

The sequence obeys the rule: "The concatenation of a(n) and a(a(n)) is odd". Example: "1" and the 1st term, concatenated, is 11; "3" and the 3rd term, concatenated, is 35; "5" and the 5th term, concatenated, is 57; "2" and the 2nd term, concatenated, is 23; etc.

Links

Table of n, a(n) for n=1..71.

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.

B. 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 >= 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)

Crossrefs

Equals A080032 + 1. Cf. A079000, A079250-A079259, A080029-A080031.

Sequence in context: A210042 A338872 A274421 * A125132 A352849 A243352

Adjacent sequences: A079310 A079311 A079312 * A079314 A079315 A079316

Keyword

easy,nonn,changed

Author

J. C. Lagarias and N. J. A. Sloane, Feb 11 2003

Extensions

More terms from Matthew Vandermast, Mar 20 2003

Status

approved