The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A080032

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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".
(history; published version)

#20 by Michel Marcus at Sat Apr 13 01:46:01 EDT 2024

STATUS

reviewed

approved

#19 by Joerg Arndt at Sat Apr 13 01:45:29 EDT 2024

STATUS

proposed

reviewed

#18 by Chai Wah Wu at Sat Apr 13 00:32:11 EDT 2024

STATUS

editing

proposed

#17 by Chai Wah Wu at Sat Apr 13 00:32:06 EDT 2024

LINKS

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

FORMULA

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)

STATUS

approved

editing

#16 by N. J. A. Sloane at Thu Mar 02 23:12:40 EST 2017

STATUS

editing

approved

#15 by N. J. A. Sloane at Thu Mar 02 23:12:37 EST 2017

COMMENTS

The same sequence, but without the initial 0, obeis 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

STATUS

proposed

editing

#14 by Michel Marcus at Thu Mar 02 14:37:43 EST 2017

STATUS

editing

proposed

#13 by Michel Marcus at Thu Mar 02 14:37:30 EST 2017

LINKS

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/indexVOL6/Cloitre/cloitre2.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.

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.NT/0305308) [math.NT], 2003.

STATUS

proposed

editing

Discussion

Thu Mar 02

14:37

Michel Marcus: Please sign new comment.

#12 by Eric Angelini at Thu Mar 02 06:06:26 EST 2017

STATUS

editing

proposed

#11 by Joerg Arndt at Wed Feb 22 12:25:18 EST 2017

STATUS

proposed

editing

Discussion

Wed Mar 01

17:29

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