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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 ) = ceiling( n / 5! ). a(n) = A030299(n+153). a(n) == 3 (mod 9). a(n) = 3 + 9*A178486(n). MATHEMATICA Take[FromDigits/@Permutations[Range], 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 October 3 11:41 EDT 2022. Contains 357231 sequences. (Running on oeis4.)