A273492 -id:A273492 - cp's OEIS frontend

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

Altug Alkan, Aug 29 2016

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)

			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.

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

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

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

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

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, ", ")));

A275772 Average values of different permutations of digits of A275945(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 11, 22, 33, 44, 55, 22, 33, 44, 55, 66, 22, 33, 44, 55, 66, 33, 44, 55, 66, 77, 33, 44, 55, 66, 77, 44, 55, 66, 77, 88, 44, 55, 66, 77, 88, 55, 66, 77, 88, 99, 37, 74, 111, 148, 185, 222, 259, 296, 333, 370, 74, 111, 148, 185, 222, 259

Offset: 1

Altug Alkan, Aug 29 2016

			a(10) = 11 because A275945(10) = 11.
a(11) = 22 because A275945(11) = 13 and (13+31)/2 = 22.
a(12) = 33 because A275945(12) = 15 and (15+51)/2 = 33.

Altug Alkan, Table of n, a(n) for n = 1..20000

Cf. A007953, A055642, A273492, A275945.

A055642(n) = #Str(n);
A007953(n) = sumdigits(n);
a(n) = ((10^A055642(n)-1)/9)*(A007953(n)/A055642(n));
for(n=1, 1e3, if((((10^A055642(n)-1)/9)*A007953(n)) % A055642(n) == 0, print1(a(n), ", ")));

cp's OEIS Frontend

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

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