##
**
Numerical Analogues of Aronson's Sequence
**

###
Benoit Cloitre

13 rue Pinaigrier

Tours 37000

FRANCE

N. J. A. Sloane

AT\&T Shannon Labs

Florham Park, NJ 07932-0971

USA

Matthew J. Vandermast

53 Piaget Avenue

Clifton, NJ 07011-1216

USA

**Abstract:**
Aronson's sequence 1, 4, 11, 16, ... is defined by the English sentence
"t is the first, fourth, eleventh, sixteenth, ... letter
of this sentence."
This paper introduces some numerical analogues, such as:
*a(n)* is taken to be the smallest positive integer greater
than *a*(*n*-1) which is consistent with the condition
"*n* is a member of the sequence if and only if *a(n)* is odd."
This sequence can also be characterized by its "square",
the sequence *a^(2) (n) = a(a(n))*, which equals 2*n*+3 for *n* >= 1.
There are many generalizations of this sequence,
some of which are new, while others throw new light
on previously known sequences.

**
Full version: pdf,
dvi,
ps,
latex
**

(Concerned with sequences
A005224
A001462
A079000
A079948
A080596
A079313
A079253
A081023
A080653
A079325
A079257
A079258
A079254
A014132
A000217
A003605
A006166
A080637
A079882
A007378
A080780
A080588
A080591
A000201
A080760
A010906
A080759
A080746
A079255
A079259
.)

Received March 31, 2003;
revised version received July 2, 2003.
Published in *Journal of Integer Sequences* July 4, 2003.

Return to
**Journal of Integer Sequences home page**