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A371463
Numbers such that the arithmetic mean of its digits is equal to twice the population standard deviation of its digits.
2
0, 13, 26, 31, 39, 62, 93, 1133, 1313, 1331, 1779, 1797, 1977, 2266, 2626, 2662, 3113, 3131, 3311, 3399, 3939, 3993, 6226, 6262, 6622, 7179, 7197, 7719, 7791, 7917, 7971, 9177, 9339, 9393, 9717, 9771, 9933, 10111, 11011, 11101, 11110, 11123, 11132, 11213, 11231
OFFSET
1,2
COMMENTS
Equivalently, numbers whose digits have the coefficient of variation (or relative population standard deviation) equal to 1/2.
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
1133 is a term since the mean of the digits is (1 + 1 + 3 + 3)/4 = 2 and the standard deviation of the digits is sqrt(((1-2)^2 + (1-2)^2 + (3-2)^2 + (3-2)^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, 12000], Mean[IntegerDigits[#]]==2DigStd[#]&]
PROG
(Python)
from itertools import count, islice
def A371463_gen(startvalue=0): # generator of terms >= startvalue
return filter(lambda n:5*sum(s:=tuple(map(int, str(n))))**2 == len(s)*sum(d**2 for d in s)<<2, count(max(startvalue, 0)))
A371463_list = list(islice(A371463_gen(), 20)) # Chai Wah Wu, Mar 30 2024
KEYWORD
nonn,base
AUTHOR
Stefano Spezia, Mar 24 2024
STATUS
approved