cp's OEIS Frontend

A371464 Numbers such that the arithmetic mean of its digits is equal to three times the population standard deviation of its digits.

%I A371464 #15 Mar 30 2024 15:56:52
%S A371464 0,12,21,24,36,42,48,63,84,1122,1212,1221,2112,2121,2211,2244,2424,
%T A371464 2442,2556,2565,2655,3366,3447,3474,3636,3663,3744,4224,4242,4347,
%U A371464 4374,4422,4437,4473,4488,4734,4743,4848,4884,5256,5265,5526,5562,5625,5652,6255,6336,6363
%N A371464 Numbers such that the arithmetic mean of its digits is equal to three times the population standard deviation of its digits.
%C A371464 Equivalently, numbers whose digits have the coefficient of variation (or relative population standard deviation) equal to 1/3.
%C A371464 Any number obtained without leading zeros from a permutation of the digits of a given term of the sequence is also a term.
%C A371464 The concatenation of several copies of any term is a term. - _Robert Israel_, Mar 24 2024
%H A371464 Wikipedia, <a href="https://en.wikipedia.org/wiki/Coefficient_of_variation">Coefficient of variation</a>.
%H A371464 Wikipedia, <a href="https://en.wikipedia.org/wiki/Standard_deviation">Standard deviation</a>.
%e A371464 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.
%t A371464 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[#]&]
%o A371464 (Python)
%o A371464 from itertools import count, islice
%o A371464 def A371464_gen(startvalue=0): # generator of terms >= startvalue
%o A371464     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)))
%o A371464 A371464_list = list(islice(A371464_gen(),20)) # _Chai Wah Wu_, Mar 30 2024
%Y A371464 Cf. A371383, A371384, A371462, A371463.
%Y A371464 Cf. A238619, A238620, A238658, A238660, A238662.
%K A371464 nonn,base
%O A371464 1,2
%A A371464 _Stefano Spezia_, Mar 24 2024