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A371464
Numbers such that the arithmetic mean of its digits is equal to three times the population standard deviation of its digits.
2
0, 12, 21, 24, 36, 42, 48, 63, 84, 1122, 1212, 1221, 2112, 2121, 2211, 2244, 2424, 2442, 2556, 2565, 2655, 3366, 3447, 3474, 3636, 3663, 3744, 4224, 4242, 4347, 4374, 4422, 4437, 4473, 4488, 4734, 4743, 4848, 4884, 5256, 5265, 5526, 5562, 5625, 5652, 6255, 6336, 6363
OFFSET
1,2
COMMENTS
Equivalently, numbers whose digits have the coefficient of variation (or relative population standard deviation) equal to 1/3.
Any number obtained without leading zeros from a permutation of the digits of a given term of the sequence is also a term.
The concatenation of several copies of any term is a term. - Robert Israel, Mar 24 2024
EXAMPLE
2244 is a term since the mean of the digits is (2 + 2 + 4 + 4)/4 = 3 and the standard deviation of the digits is sqrt(((2-3)^2 + (2-3)^2 + (4-3)^2 + (4-3)^2)/4) = 1.
MATHEMATICA
DigStd[n_]:=If[n==0||IntegerLength[n]==1, 0, Sqrt[(IntegerLength[n]-1)/IntegerLength[n]]StandardDeviation[IntegerDigits[n]]]; Select[Range[0, 6400], Mean[IntegerDigits[#]]==3DigStd[#]&]
PROG
(Python)
from itertools import count, islice
def A371464_gen(startvalue=0): # generator of terms >= startvalue
return filter(lambda n:10*sum(s:=tuple(map(int, str(n))))**2 == 9*len(s)*sum(d**2 for d in s), count(max(startvalue, 0)))
A371464_list = list(islice(A371464_gen(), 20)) # Chai Wah Wu, Mar 30 2024
KEYWORD
nonn,base
AUTHOR
Stefano Spezia, Mar 24 2024
STATUS
approved