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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
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 ) = ceiling( 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
KEYWORD
fini,full,easy,nonn,base
AUTHOR
M. F. Hasler, May 28 2010
STATUS
approved