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

10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 61, 63, 65, 67, 69, 70, 72, 74, 76, 78, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 1000, 1001, 1002, 1004, 1005, 1006, 1008, 1009, 1010, 1011, 1013, 1014, 1015, 1017, 1018, 1019, 1020, 1022, 1023, 1024

Offset: 1

Author

Altug Alkan, Aug 29 2016

Keywords

• easy
• base
• nonn

Comments

Complement of A275945.

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.).

From Robert Israel, Sep 01 2016: (Start)

n such that A002275(A055642(n))*A007953(n) is not divisible by A055642(n).

In particular, contains no k-digit numbers if k is in A014950. (End)

Examples

			12 is a term because (12+21) = 33 is not divisible by 2.
1000 is a term because (1+10+100+1000) = 1111 is not divisible by 4.
123 is not a term because (123+132+213+231+312+321) is divisible by 6.
1001 is a term because (11+101+110+1001+1010+1100) is not divisible by 6.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002275, A014950, A055642, A066642, A007953, A045876, A055642, A275945.

Programs

Maple

f:= proc(n) local L,d,s;
  L:= convert(n,base,10);
  d:= nops(L);
  s:= convert(L,`+`);
  evalb(s*(10^d-1)/9 mod d = 0)
end proc:
remove(f, [$1..10000]); # Robert Israel, Sep 01 2016

Mathematica

Select[Range[2^10], ! IntegerQ@ Mean@ Map[FromDigits, Permutations@ #] &@ IntegerDigits@ # &] (* Michael De Vlieger, Aug 29 2016 *)

PARI

A055642(n) = #Str(n);
A007953(n) = sumdigits(n);
for(n=1, 2000, if((((10^A055642(n)-1)/9)*A007953(n)) % A055642(n) != 0, print1(n, ", ")));