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 A178475 Permutations of 12345: Numbers having each of the decimal digits 1,...,5 exactly once, and no other digit. 6
 12345, 12354, 12435, 12453, 12534, 12543, 13245, 13254, 13425, 13452, 13524, 13542, 14235, 14253, 14325, 14352, 14523, 14532, 15234, 15243, 15324, 15342, 15423, 15432, 21345, 21354, 21435, 21453, 21534, 21543, 23145, 23154, 23415 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS There are 5! = 120 terms in this finite subsequence of A030299. It would be interesting to conceive simple and/or efficient functions which yield (a) the n-th term of this sequence: f(n) = a(n), (b) for a given term, the subsequent one: f(a(n)) = a(1 + n (mod 5!)). From Nathaniel Johnston, May 19 2011: (Start) Individual terms a(n) can be computed efficiently via the following procedure: Define b(n,k) = 1 + floor(((n-1) mod (k+1)!)/k!) for k = 1, 2, 3, 4. The first digit of a(n) is b(n,4). The second digit of a(n) is the b(n,3)-th number not already used. The third digit of a(n) is the b(n,2)-th number not already used. The fourth digit of a(n) is the b(n,1)-th number not already used, and the final digit of a(n) is the only digit remaining. This procedure generalizes in the obvious way for related sequences such as A178476. For example, if n = 38 then we compute b(38,1) = 2, b(38,2) = 1, b(38,3) = 3, b(38,4) = 2. Thus a(38) = 24153 (2, followed by the 3rd digit not yet used, followed by the 1st digit not yet used, followed by the 2nd digit not yet used, followed by the last remaining digit). (End) LINKS Nathaniel Johnston, Table of n, a(n) for n = 1..120 (full sequence) FORMULA a(n) + a(5!+1-n) = 66666. floor( a(n) / 10^4 ) = ceil( n / 4! ). a(n) = A030299(n+33). a(n) == 6 (mod 9). a(n) = 6 + 9*A178485(n). MATHEMATICA FromDigits/@Permutations[Range[5]] (* Harvey P. Dale, Jan 19 2019 *) PROG (PARI) A178475(n)={my(b=vector(4, k, 1+(n-1)%(k+1)!\k!), t=b[4], d=vector(4, i, i+(i>=t))); for(i=1, 3, t=10*t+d[b[4-i]]; d=vecextract(d, Str("^"b[4-i]))); t*10+d[1]} \\ - M. F. Hasler (following N. Johnston's comment), Jan 10 2012 (PARI) v=vector(5, i, 10^(i-1))~; A178475=vecsort(vector(5!, i, numtoperm(5, i)*v)) is_A178475(x)={ vecsort(Vecsmall(Str(x)))==Vecsmall("12345") } forstep( m=12345, 54321, 9, is_A178475(m) & print1(m", ")) CROSSREFS Cf. A030298, A030299, A055089, A060117, A178476. Sequence in context: A248717 A184472 A251949 * A104972 A193493 A091341 Adjacent sequences:  A178472 A178473 A178474 * A178476 A178477 A178478 KEYWORD fini,full,easy,nonn,base,changed AUTHOR M. F. Hasler, May 28 2010 STATUS approved

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Last modified January 19 23:25 EST 2019. Contains 319319 sequences. (Running on oeis4.)