A178485 -id:A178485 - cp's OEIS frontend

A178475 Permutations of 12345: Numbers having each of the decimal digits 1,...,5 exactly once, and no other digit.

12345, 12354, 12435, 12453, 12534, 12543, 13245, 13254, 13425, 13452, 13524, 13542, 14235, 14253, 14325, 14352, 14523, 14532, 15234, 15243, 15324, 15342, 15423, 15432, 21345, 21354, 21435, 21453, 21534, 21543, 23145, 23154, 23415

Offset: 1

M. F. Hasler, May 28 2010

There are 5! = 120 terms in this finite subsequence of A030299.
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 5!)).
From Nathaniel Johnston, May 19 2011: (Start)
Individual terms a(n) can be computed efficiently via the following procedure: Define b(n,k) = 1 + floor(((n-1) mod (k+1)!)/k!) for k = 1, 2, 3, 4. The first digit of a(n) is b(n,4). The second digit of a(n) is the b(n,3)-th number not already used. The third digit of a(n) is the b(n,2)-th number not already used. The fourth digit of a(n) is the b(n,1)-th number not already used, and the final digit of a(n) is the only digit remaining. This procedure generalizes in the obvious way for related sequences such as A178476.
For example, if n = 38 then we compute b(38,1) = 2, b(38,2) = 1, b(38,3) = 3, b(38,4) = 2. Thus a(38) = 24153 (2, followed by the 3rd digit not yet used, followed by the 1st digit not yet used, followed by the 2nd digit not yet used, followed by the last remaining digit).
(End)

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

Cf. A030298, A030299, A055089, A060117, A178476.

FromDigits/@Permutations[Range[5]] (* Harvey P. Dale, Jan 19 2019 *)

A178475(n)={my(b=vector(4,k,1+(n-1)%(k+1)!\k!),t=b[4],d=vector(4,i,i+(i>=t)));for(i=1,3,t=10*t+d[b[4-i]];d=vecextract(d,Str("^"b[4-i])));t*10+d[1]} \\ - M. F. Hasler (following N. Johnston's comment), Jan 10 2012

v=vector(5,i,10^(i-1))~; A178475=vecsort(vector(5!,i,numtoperm(5,i)*v))
is_A178475(x)={ vecsort(Vecsmall(Str(x)))==Vecsmall("12345") }
forstep( m=12345,54321,9, is_A178475(m) & print1(m","))

a(n) + a(5! + 1 - n) = 66666.
floor( a(n) / 10^4 ) = ceiling( n / 4! ).
a(n) = A030299(n+33).
a(n) == 6 (mod 9).
a(n) = 6 + 9*A178485(n).

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).

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

A178475 Permutations of 12345: Numbers having each of the decimal digits 1,...,5 exactly once, and no other digit.

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

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A191820 A178478(n)/9.

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

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