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 A160818 Each number is the average of the numbers formed by all the possible permutations of the digits of that number. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS H. v. Eitzen, Table of n, a(n) for n=1..1002 Robert Munafo, Equal to Average of Permutations of its Digits [From Robert Munafo, Jun 18 2009] EXAMPLE a(22) = 370 is a member because 073+037+307+370+703+730 = 2220, average = 2220/6 = 370 MAPLE 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 PROG (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 CROSSREFS Sequence in context: A248954 A082937 A214019 * A244514 A082810 A344550 Adjacent sequences:  A160815 A160816 A160817 * A160819 A160820 A160821 KEYWORD nonn,base AUTHOR Claudio Meller, May 27 2009 EXTENSIONS 15 more terms from R. J. Mathar, May 29 2009 More terms from Robert Munafo, Jun 18 2009 STATUS approved

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Last modified September 24 19:27 EDT 2021. Contains 347651 sequences. (Running on oeis4.)