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A178476 Permutations of 123456: Numbers having each of the decimal digits 1,...,6 exactly once, and no other digit. 5
123456, 123465, 123546, 123564, 123645, 123654, 124356, 124365, 124536, 124563, 124635, 124653, 125346, 125364, 125436, 125463, 125634, 125643, 126345, 126354, 126435, 126453, 126534, 126543, 132456, 132465, 132546, 132564, 132645, 132654 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This finite sequence contains 6!=720 terms.

This is a subsequence of A030299, consisting of elements A030299[154]...A030299[873].

If individual digits are be split up into separate terms, we get a subsequence of A030298.

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 6! ]).

The expression a(n+6)-a(n) takes only 18 different values, for n=1...6!-6.

An efficient procedure for generating the n-th term of this sequence can be found at A178475. - Nathaniel Johnston, May 19 2011

From Hieronymus Fischer, Feb 13 2013: (Start)

The sum of all terms as decimal numbers is 279999720.

General formula for the sum of all terms (interpreted as decimal permutational numbers with exactly d different digits from the range 1..d<10): sum = (d+1)!*(10^d-1)/18.

If the terms are interpreted as base-7 numbers the sum is 49412160.

General formula for the sum of all terms of the corresponding sequence of base-p permutational numbers (numbers with exactly p-1 different digits excluding the zero digit): sum = (p-2)!*(p^p-p)/2. (End)

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..720 (full sequence)

FORMULA

a(n) + a(6!+1-n) = 777777.

floor( a(n) / 10^5 ) = ceil( n / 5! ).

a(n)=A030299(n+153).

a(n)==3 (mod 9).

a(n)=3+9*A178486(n).

MATHEMATICA

Take[FromDigits/@Permutations[Range[6]], 40] (* Harvey P. Dale, Jun 05 2012 *)

PROG

(PARI) v=vector(6, i, 10^(i-1))~; A178476=vecsort(vector(6!, i, numtoperm(6, i)*v));

is_A178476(x)= { vecsort(Vec(Str(x)))==Vec("123456") }

forstep( m=123456, 654321, 9, is_A178476(m) & print1(m", "))

CROSSREFS

Cf. A030298, A030299, A055089, A060117.

Sequence in context: A254017 A254024 A254891 * A104973 A077301 A209734

Adjacent sequences:  A178473 A178474 A178475 * A178477 A178478 A178479

KEYWORD

fini,full,easy,nonn,base

AUTHOR

M. F. Hasler, May 28 2010

STATUS

approved

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Last modified November 20 21:38 EST 2018. Contains 317422 sequences. (Running on oeis4.)