

A030299


Decimal representation of permutations of lengths 1, 2, 3, ... arranged lexicographically.


31



1, 12, 21, 123, 132, 213, 231, 312, 321, 1234, 1243, 1324, 1342, 1423, 1432, 2134, 2143, 2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 3412, 3421, 4123, 4132, 4213, 4231, 4312, 4321, 12345, 12354, 12435, 12453, 12534, 12543, 13245, 13254, 13425
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OFFSET

1,2


COMMENTS

This is a list of the permutations in "oneline" notation (cf. Dixon and Mortimer, p. 2). The ith element of the string is the image of i under the permutation. For example 231 is the permutation that sends 1 to 2, 2 to 3, and 3 to 1.  N. J. A. Sloane, Apr 12 2014
Precise definition of the term "Decimal representation" (required for indices n>409113): Numbers N(s) = Sum_{i=1..m} s(i)*10^(mi), where s runs over the permutations of (1,...,m), and m=1,2,3,.... This also defines the "lexicographical" order: Obviously 21 comes before 123, etc. The lexicographical order of the permutations, for given m, is the same as the natural order of the numbers N(s).  M. F. Hasler, Jan 28 2013
An alternate variant, using concatenation of the permutations, is very clumsy once the length exceeds 9. For example, after 987654321 (= A030299(409113), where 409113 = A007489(9)) we would get 12345678910, 12345678109, ... In A030298 this problem has been avoided by listing the elements of permutations as separate terms. [Edited by M. F. Hasler, Dec 2012 and Jan 28 2013]
Sequence A051845 is a baseindependent version of this sequence: Permutations of 1...m are considered as numbers written in base m+1.  M. F. Hasler, Jan 28 2013


REFERENCES

Dixon, John D.; Mortimer, Brian. Permutation groups. Graduate Texts in Mathematics, 163. SpringerVerlag, New York, 1996. xii+346 pp. ISBN: 0387945997 MR1409812 (98m:20003).


LINKS

A. Karttunen, Table of n, a(n) for n = 1..5913
OEIS Wiki, Discussion about alternate definition(s) of this sequence, started by M. F. Hasler, Jan 28 2013
Index entries for sequences related to permutations


MAPLE

seq(seq(add(s[i]*10^(mi), i=1..m), s=combinat:permute([$1..m])), m=1..5); # Robert Israel, Oct 14 2015


MATHEMATICA

Flatten @ Table[FromDigits /@ Permutations[Table[i, {i, n}]], {n, 9}] (* For first 409113 terms; Zak Seidov, Oct 03 2015 *)


PROG

(PARI) is_A030299(n)={ (n>1234567890 & print("maybe"))  vecsort(digits(n))==vector(#Str(n), i, i) } \\ /* use digits(n)=eval(Vec(Str(n))) in older versions lacking this function */ \\ M. F. Hasler, Dec 12 2012
(MIT/GNU Scheme from Antti Karttunen, Dec 18 2012):
;; Requires also code from A030298 and A055089:
(define (A030299 n) (vector>basek (A030298permvec (A084556 n) (A220660 n)) 10))
(define (vector>basek vec k) (let loop ((i 0) (s 0)) (cond ((= (vectorlength vec) i) s) ((>= (vectorref vec i) k) (error (format #f "Cannot interpret vector ~a in base ~a!" vec k))) (else (loop (+ i 1) (+ (* k s) (vectorref vec i)))))))


CROSSREFS

A007489(n) gives the position (index) of the term corresponding to last permutation of n elements: (n,n1,...,1).
The first differences A220664 has interesting fractal structure, see A219664 and A217626.
Cf. also A030298, A055089, A060117, A181073.
See A240763 for preferential arrangements.
Sequence in context: A321771 A225864 A134514 * A268532 A260275 A001292
Adjacent sequences: A030296 A030297 A030298 * A030300 A030301 A030302


KEYWORD

nonn,easy,base


AUTHOR

N. J. A. Sloane, Clark Kimberling


EXTENSIONS

Edited by N. J. A. Sloane, Feb 23 2010


STATUS

approved



