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A051845 Table in which n-th row gives all permutations of digits 1..n interpreted in base n+1. 7
1, 5, 7, 27, 30, 39, 45, 54, 57, 194, 198, 214, 222, 238, 242, 294, 298, 334, 346, 358, 366, 414, 422, 434, 446, 482, 486, 538, 542, 558, 566, 582, 586, 1865, 1870, 1895, 1905, 1930, 1935, 2045, 2050, 2105, 2120, 2140, 2150, 2255, 2265, 2285, 2300, 2355 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

All terms in any odd row 2n+1 are divisible by 2n+1.

Variant of permutational numbers with shifted digits 0->1->2->...->k+1 in k+1 positional system - see A134750 - Artur Jasinski, Nov 08 2007

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

n-th row n has n! elements: 1; 5, 7; 27, 30, 39, 45, 54, 57; E.g. the permutations of digits 1, 2 and 3 in lexicographic order are 123, 132, 213, 231, 312, 321 which interpreted in base 4 give the fourth row of the table: 27, 30, 39, 45, 54, 57

MAPLE

with(combinat, permute); compute_u_rows := proc(u) local a, n; a := []; for n from 1 to u do a := [op(a), op(map(list_in_base_b, permute(n), (n+1)))]; od; RETURN(a); end; list_in_base_b := proc(l, b) local k; add(l[nops(l)-k]*(b^k), k=0..(nops(l)-1)); end;

MATHEMATICA

(*A051845*); a = {}; b = {}; Do[AppendTo[b, n]; w = Permutations[b]; Do[j = FromDigits[1 + w[[m]], n + 2]; AppendTo[a, j], {m, 1, Length[w]}], {n, 0, 5}]; a - Artur Jasinski, Nov 08 2007

CROSSREFS

Left edge = A023811, right edge = A051846.

Cf. A134640, A134750.

Sequence in context: A324363 A166100 A135606 * A278646 A029668 A144392

Adjacent sequences:  A051842 A051843 A051844 * A051846 A051847 A051848

KEYWORD

easy,nonn,tabf,base

AUTHOR

Antti Karttunen, Dec 13 1999

STATUS

approved

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Last modified March 21 01:18 EDT 2019. Contains 321356 sequences. (Running on oeis4.)