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A273492 Numbers n such that the average of different permutations of digits of n is not an integer.

%I A273492 #31 Sep 03 2016 16:56:48
%S A273492 10,12,14,16,18,21,23,25,27,29,30,32,34,36,38,41,43,45,47,49,50,52,54,
%T A273492 56,58,61,63,65,67,69,70,72,74,76,78,81,83,85,87,89,90,92,94,96,98,
%U A273492 1000,1001,1002,1004,1005,1006,1008,1009,1010,1011,1013,1014,1015,1017,1018,1019,1020,1022,1023,1024
%N A273492 Numbers n such that the average of different permutations of digits of n is not an integer.
%C A273492 Complement of A275945.
%C A273492 Permutations with a first digit of 0 are included in the average (i.e. 0010 is taken to be 10, 01 is taken to be 1, etc.).
%C A273492 From _Robert Israel_, Sep 01 2016: (Start)
%C A273492 n such that A002275(A055642(n))*A007953(n) is not divisible by A055642(n).
%C A273492 In particular, contains no k-digit numbers if k is in A014950. (End)
%H A273492 Robert Israel, <a href="/A273492/b273492.txt">Table of n, a(n) for n = 1..10000</a>
%e A273492 12 is a term because (12+21) = 33 is not divisible by 2.
%e A273492 1000 is a term because (1+10+100+1000) = 1111 is not divisible by 4.
%e A273492 123 is not a term because (123+132+213+231+312+321) is divisible by 6.
%e A273492 1001 is a term because (11+101+110+1001+1010+1100) is not divisible by 6.
%p A273492 f:= proc(n) local L,d,s;
%p A273492   L:= convert(n,base,10);
%p A273492   d:= nops(L);
%p A273492   s:= convert(L,`+`);
%p A273492   evalb(s*(10^d-1)/9 mod d = 0)
%p A273492 end proc:
%p A273492 remove(f, [$1..10000]); # _Robert Israel_, Sep 01 2016
%t A273492 Select[Range[2^10], ! IntegerQ@ Mean@ Map[FromDigits, Permutations@ #] &@ IntegerDigits@ # &] (* _Michael De Vlieger_, Aug 29 2016 *)
%o A273492 (PARI) A055642(n) = #Str(n);
%o A273492 A007953(n) = sumdigits(n);
%o A273492 for(n=1, 2000, if((((10^A055642(n)-1)/9)*A007953(n)) % A055642(n) != 0, print1(n, ", ")));
%Y A273492 Cf. A002275, A014950, A055642, A066642, A007953, A045876, A055642, A275945.
%K A273492 easy,base,nonn
%O A273492 1,1
%A A273492 _Altug Alkan_, Aug 29 2016