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A160818
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Each number is the average of the addition of all the possible permutations of the digits of that number.
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3
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1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 370, 407, 444, 481, 518, 555, 592, 629, 666, 777, 888, 999, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 111111
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OFFSET
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1,2
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COMMENTS
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For example with 370: 073+037+307+370+703+730 = 2220, average = 2220/6 = 370
A number n with k digits and digit sum s occurs in the sequence if and only if (10^k-1)*s = 9*k*n. [From Hagen von Eitzen, Jun 17 2009]
Many terms (perhaps all) are related to decimal expansions of fractions with a power of 3 in the denominator (see Munafo webpage) [From Robert Munafo, Jun 18 2009]
Replacing "all possible permutations" in the definition with "all cyclic permutations" produces the same sequence. Even more generally, the symmetric group can be replaced by any finite group operating transitively on the n places. [From Hagen von Eitzen, Jun 22 2009]
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LINKS
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H. v. Eitzen, Table of n, a(n) for n=1..1002
R. Munafo, Equal to Average of Permutations of its Digits [From Robert Munafo, Jun 18 2009]
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MAPLE
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Lton := proc(L) add( op(i, L)*10^(i-1), i=1..nops(L)) ; end: isA160818 := proc(n) local dgs, av ; dgs := combinat[permute]( convert(n, base, 10) ); av := add( Lton(p), p=dgs)/nops(dgs) ; RETURN(av=n) ; end: for n from 1 to 40000 do if isA160818(n) then printf("%d, ", n) ; fi; od: [From R. J. Mathar, May 29 2009]
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PROG
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(Other) /* Easily optimized; see C source code on the Munafo web page */ [From Robert Munafo, Jun 18 2009]
(PARI) for(k=1, 20, rep=(10^k-1)/9; for(s=1, 9*k, if((rep*s)%k==0&&A007953(n=rep*s/k)==s, print(n)))) [From Hagen von Eitzen, Jun 22 2009]
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CROSSREFS
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Sequence in context: A193408 A082937 A214019 * A082810 A010785 A032573
Adjacent sequences: A160815 A160816 A160817 * A160819 A160820 A160821
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KEYWORD
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nonn,base
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AUTHOR
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Claudio Meller, May 27 2009
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EXTENSIONS
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15 more terms from R. J. Mathar, May 29 2009
More terms from Robert Munafo, Jun 18 2009
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STATUS
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approved
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