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A273492 Numbers n such that the average of different permutations of digits of n is not an integer. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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)

LINKS

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

EXAMPLE

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.

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 *)

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, A055642, A066642, A007953, A045876, A055642, A275945.

Sequence in context: A318700 A180157 A309539 * A227870 A007958 A179083

Adjacent sequences:  A273489 A273490 A273491 * A273493 A273494 A273495

KEYWORD

easy,base,nonn

AUTHOR

Altug Alkan, Aug 29 2016

STATUS

approved

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Last modified June 4 10:04 EDT 2020. Contains 334825 sequences. (Running on oeis4.)