A275945 Numbers n such that the average of different permutations of digits of n is an integer.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 19, 20, 22, 24, 26, 28, 31, 33, 35, 37, 39, 40, 42, 44, 46, 48, 51, 53, 55, 57, 59, 60, 62, 64, 66, 68, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 91, 93, 95, 97, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111

Offset

1,2

Comments

Complement of 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.).

From Robert Israel, Sep 01 2016: (Start)

n such that A002275(A055642(n))*A007953(n) is divisible by A055642(n).

In particular, contains all k-digit numbers if k is in A014950. (End)

Links

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

Example

97 is a term because (97+79) is divisible by 2.
100 is a term because (1+10+100) is divisible by 3.
123 is a term because (123+132+213+231+312+321) is divisible by 6.
1001 is not a term because (11+101+110+1001+1010+1100) is not divisible by 6.

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:
select(f, [$1..10000]); # Robert Israel, Sep 01 2016

Mathematica

Select[Range@ 111, IntegerQ@ Mean@ Map[FromDigits, Permutations@ #] &@ IntegerDigits@ # &] (* Michael De Vlieger, Aug 29 2016 *)

Prog

(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, ", ")));

Crossrefs

Cf. A002275, A014950, A045876, A055642, A066642, A007953, A273492.

Sequence in context: A185660 A191839 A032959 * A061383 A059708 A306520

Adjacent sequences: A275942 A275943 A275944 * A275946 A275947 A275948

Keyword

easy,base,nonn

Author

Altug Alkan, Aug 29 2016

Status

approved