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A160818
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Each number is the average of the numbers formed by 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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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. - 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). - 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. - Hagen von Eitzen, Jun 22 2009
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LINKS
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EXAMPLE
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a(22) = 370 is a member because 073+037+307+370+703+730 = 2220, average = 2220/6 = 370
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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: # R. J. Mathar, May 29 2009
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PROG
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(C) See Robert Munafo link
(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, print1(n, ", ")))) \\ Hagen von Eitzen, Jun 22 2009
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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