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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
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
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
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