

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
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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 nth 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(((n1) 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 ) = ceiling( 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+(n1)%(k+1)!\k!), t=b[4], d=vector(4, i, i+(i>=t))); for(i=1, 3, t=10*t+d[b[4i]]; d=vecextract(d, Str("^"b[4i]))); t*10+d[1]} \\  M. F. Hasler (following N. Johnston's comment), Jan 10 2012
(PARI) v=vector(5, i, 10^(i1))~; 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



