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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is a list of the permutations in "one-line" notation (cf. Dixon and Mortimer, p. 2). The i-th 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^(m-i), 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 base-independent 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. Springer-Verlag, New York, 1996. xii+346 pp. ISBN: 0-387-94599-7 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 MAPLE seq(seq(add(s[i]*10^(m-i), 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->base-k (A030298permvec (A084556 n) (A220660 n)) 10)) (define (vector->base-k vec k) (let loop ((i 0) (s 0)) (cond ((= (vector-length vec) i) s) ((>= (vector-ref vec i) k) (error (format #f "Cannot interpret vector ~a in base ~a!" vec k))) (else (loop (+ i 1) (+ (* k s) (vector-ref vec i))))))) CROSSREFS A007489(n) gives the position (index) of the term corresponding to last permutation of n elements: (n,n-1,...,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 EXTENSIONS Edited by N. J. A. Sloane, Feb 23 2010 STATUS approved

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Last modified February 26 03:09 EST 2020. Contains 332272 sequences. (Running on oeis4.)