A160818 Each number is the average of the numbers formed by all the possible permutations of the digits of that number.

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

Author

Claudio Meller, May 27 2009

Keywords

• nonn
• base

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

Examples

			a(22) = 370 is a member because 073+037+307+370+703+730 = 2220, average = 2220/6 = 370
		

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]

Programs

C

See Robert Munafo link

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

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

Extensions

15 more terms from R. J. Mathar, May 29 2009

More terms from Robert Munafo, Jun 18 2009