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A273492
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Numbers n such that the average of different permutations of digits of n is not an integer.
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3
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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
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OFFSET
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1,1
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COMMENTS
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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.).
In particular, contains no k-digit numbers if k is in A014950. (End)
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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Select[Range[2^10], ! IntegerQ@ Mean@ Map[FromDigits, Permutations@ #] &@ IntegerDigits@ # &] (* Michael De Vlieger, Aug 29 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,base,nonn
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AUTHOR
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STATUS
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approved
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