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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).

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

AUTHOR

M. F. Hasler, May 28 2010

STATUS

approved

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Last modified November 16 02:33 EST 2018. Contains 317252 sequences. (Running on oeis4.)