A178486 -id:A178486 - cp's OEIS frontend

A178476 Permutations of 123456: Numbers having each of the decimal digits 1,...,6 exactly once, and no other digit.

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

M. F. Hasler, May 28 2010

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)

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

Cf. A030298, A030299, A055089, A060117.

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

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","))

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).

A178485 (A178475(n)-6)/9.

Original entry on oeis.org

1371, 1372, 1381, 1383, 1392, 1393, 1471, 1472, 1491, 1494, 1502, 1504, 1581, 1583, 1591, 1594, 1613, 1614, 1692, 1693, 1702, 1704, 1713, 1714, 2371, 2372, 2381, 2383, 2392, 2393, 2571, 2572, 2601, 2605, 2612, 2615, 2681, 2683, 2701, 2705, 2723, 2725

Offset: 1

M. F. Hasler, May 28 2010

There are 5!=120 terms in this finite sequence. Its origin is the fact that numbers whose decimal expansion is a permutation of 12345 are all of the form 9k+6.

Nathaniel Johnston, Table of n, a(n) for n = 1..120 (full sequence)

Cf. A030298, A030299, A055089, A060117, A178486, A191819, A191820.

v=vector(5,i,10^(i-1))~; vecsort(vector(5!,i,numtoperm(5,i)*v))
is_A178475(x)= { vecsort(Vec(Str(x)))==Vec("12345") }
forstep( m=12345,54321,9, is_A178475(m) & print1(m","))

a(n) + a(5!+1-n) = 7406.
a(n) == 1, 2, 3, 4 or 5 (mod 10).
a(n+6)-a(n) is an element of { 100, 110, 111, 200, 220, 222, 679 }.
a(n+6)-a(n) = 679 iff (n-1)%24 > 17, where % denotes the remainder upon division.
a(n+6)-a(n) = 200, 220 or 222 iff (n-1)%30 > 23, i.e. n==25,...,30 (mod 30).

A191820 A178478(n)/9.

Original entry on oeis.org

1371742, 1371743, 1371752, 1371754, 1371763, 1371764, 1371842, 1371843, 1371862, 1371865, 1371873, 1371875, 1371952, 1371954, 1371962, 1371965, 1371984, 1371985, 1372063, 1372064, 1372073, 1372075, 1372084, 1372085, 1372742, 1372743, 1372752

Offset: 1

Nathaniel Johnston, Jun 24 2011

There are 8!=40320 terms in this finite sequence. Its origin is the fact that numbers whose decimal expansion is a permutation of 12345678 are all divisible by 9.

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A178485, A178486, A191819.

A191819 (A178477(n)-1)/9.

Original entry on oeis.org

137174, 137175, 137184, 137186, 137195, 137196, 137274, 137275, 137294, 137297, 137305, 137307, 137384, 137386, 137394, 137397, 137416, 137417, 137495, 137496, 137505, 137507, 137516, 137517, 138174, 138175, 138184, 138186, 138195, 138196, 138374, 138375, 138404

Offset: 1

Nathaniel Johnston, Jun 24 2011

The sequence is motivated by the fact that numbers whose decimal expansion is a permutation of 1234567 are all of the form 9k+1.

Nathaniel Johnston, Table of n, a(n) for n = 1..5040 (full sequence)

Cf. A178485, A178486, A191820.

cp's OEIS Frontend

A178476 Permutations of 123456: Numbers having each of the decimal digits 1,...,6 exactly once, and no other digit.

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A178485 (A178475(n)-6)/9.

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A191820 A178478(n)/9.

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A191819 (A178477(n)-1)/9.

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