A191820 -id:A191820 - cp's OEIS frontend

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

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).

A178486 (A178476(n)-3)/9.

Original entry on oeis.org

13717, 13718, 13727, 13729, 13738, 13739, 13817, 13818, 13837, 13840, 13848, 13850, 13927, 13929, 13937, 13940, 13959, 13960, 14038, 14039, 14048, 14050, 14059, 14060, 14717, 14718, 14727, 14729, 14738, 14739, 14917, 14918, 14947, 14951, 14958, 14961

Offset: 1

M. F. Hasler, May 28 2010

The sequence is motivated by the fact that numbers whose decimal expansion is a permutation of 123456, are all of the form 9k+3.

There are 6!=720 terms in this finite sequence.

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

Cf. A030298, A030299, A055089, A060117, A178485, A191819, A191820.

forstep( m=123456,654321/*or less*/,9, is_A178476(m) & print1(m\9",")) /*cf. A178476*/

a(n) + a(6!+1-n) = 86419.

a(n) == 0, 1, 2, 7, 8 or 9 (mod 10).

A178478 Permutations of 12345678: Numbers having each of the decimal digits 1..8 exactly once, and no other digit.

Original entry on oeis.org

12345678, 12345687, 12345768, 12345786, 12345867, 12345876, 12346578, 12346587, 12346758, 12346785, 12346857, 12346875, 12347568, 12347586, 12347658, 12347685, 12347856, 12347865, 12348567, 12348576, 12348657, 12348675, 12348756, 12348765

Offset: 1

M. F. Hasler, Oct 09 2010

It would be nice to have a simple explicit formula for the n-th term.

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

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

Cf. A030298, A030299, A055089, A060117, A178475-A178477, A191820.

Take[FromDigits/@Permutations[Range[8]],40] (* Harvey P. Dale, Oct 29 2014 *)

is_A178478(x)= { vecsort(Vec(Str(x)))==Vec("12345678") }

A178478(n)={my(b=vector(7,k,1+(n-1)%(k+1)!\k!),t=b[7], d=vector(7,i,i+(i>=t)));for(i=1,6,t=10*t+d[b[7-i]]; d=vecextract(d,Str("^"b[7-i]))); t*10+d[1]} \\ - M. F. Hasler (following N. Johnston's comment), Jan 10 2012

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.

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

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A178486 (A178476(n)-3)/9.

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A178478 Permutations of 12345678: Numbers having each of the decimal digits 1..8 exactly once, and no other digit.

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

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