Search: id:A134640
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%I A134640
%S A134640 0,1,2,5,7,11,15,19,21,27,30,39,45,54,57,75,78,99,108,114,120,135,141,
%T A134640 147,156,177,180,198,201,210,216,225,228,194,198,214,222,238,242,294,
%U A134640 298,334,346,358,366,414,422,434,446,482,486,538,542,558,566,582,586
%N A134640 Permutational numbers (numbers with k different digits in k-positional 
               system).
%C A134640 a(1) is the 1-positional system 1!=1 numbers
%C A134640 a(2) to a(3) are two=2! 2-positional system numbers
%C A134640 a(4) to a(9) are six=3! 3-positional system numbers
%C A134640 a(10) to a(33) are 24=4! 4-positional system numbers
%C A134640 a(34) to a(153) are 120=5! 5-positional system numbers
%C A134640 ...
%C A134640 There are a(!k)-a(Sum[m!,1,k])=a(A003422)-a(A007489) k-positional system 
               k! numbers
%C A134640 The name permutational numbers arises because each permutation of k elements 
               is isomorphic with one and only one of member of this sequence and 
               conversely each number in this sequence is isomorphic with one and 
               only one permutation of k elelmnts or its equivalent permutation 
               matrix.
%e A134640 We build permutational numbers:
%e A134640 a(1)=0 in unitary positional system we have only one digit 0
%e A134640 a(2)=1 because in binary positional system smaller number with two different 
               digits is 01 = 1
%e A134640 a(3)=2 because in binary positional system bigger number with two different 
               digits is 10 = 2 (binary system is over)
%e A134640 a(4)=5 because smallest number in ternary system with 3 different digits 
               is 012=5
%e A134640 a(5)=7 second number in ternary system with 3 different digits is 021=7
%e A134640 a(6)=11 third number in ternary system with 3 different digits is 102=11
%e A134640 a(7)=15 120=15
%e A134640 etc.
%t A134640 a = {}; b = {}; Do[AppendTo[b, n]; w = Permutations[b]; Do[j = FromDigits[w[[m]], 
               n + 1]; AppendTo[a, j], {m, 1, Length[w]}], {n, 0, 5}]; a (*Artur 
               Jasinski*)
%Y A134640 Cf. A003422, A007489.
%Y A134640 Sequence in context: A133436 A001225 A157001 this_sequence A032616 A006066 
               A084935
%Y A134640 Adjacent sequences: A134637 A134638 A134639 this_sequence A134641 A134642 
               A134643
%K A134640 nonn
%O A134640 1,3
%A A134640 Artur Jasinski (grafix(AT)csl.pl), Nov 05 2007, Nov 07 2007, Nov 08 2007
%E A134640 Corrected indices in examples. Replaced dashes in comments by the word 
               "to" - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 26 2009

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