cp's OEIS Frontend

A371463 Numbers such that the arithmetic mean of its digits is equal to twice the population standard deviation of its digits.

%I A371463 #19 Mar 30 2024 15:56:46
%S A371463 0,13,26,31,39,62,93,1133,1313,1331,1779,1797,1977,2266,2626,2662,
%T A371463 3113,3131,3311,3399,3939,3993,6226,6262,6622,7179,7197,7719,7791,
%U A371463 7917,7971,9177,9339,9393,9717,9771,9933,10111,11011,11101,11110,11123,11132,11213,11231
%N A371463 Numbers such that the arithmetic mean of its digits is equal to twice the population standard deviation of its digits.
%C A371463 Equivalently, numbers whose digits have the coefficient of variation (or relative population standard deviation) equal to 1/2.
%C A371463 Any number obtained without leading zeros from a permutation of the digits of a given term of the sequence is also a term.
%C A371463 The concatenation of several copies of any term is a term. - _Robert Israel_, Mar 24 2024
%H A371463 Wikipedia, <a href="https://en.wikipedia.org/wiki/Coefficient_of_variation">Coefficient of variation</a>.
%H A371463 Wikipedia, <a href="https://en.wikipedia.org/wiki/Standard_deviation">Standard deviation</a>.
%e A371463 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.
%t A371463 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[#]&]
%o A371463 (Python)
%o A371463 from itertools import count, islice
%o A371463 def A371463_gen(startvalue=0): # generator of terms >= startvalue
%o A371463     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)))
%o A371463 A371463_list = list(islice(A371463_gen(),20)) # _Chai Wah Wu_, Mar 30 2024
%Y A371463 Cf. A371383, A371384, A371462, A371464.
%Y A371463 Cf. A238619, A238620, A238658, A238660, A238662.
%K A371463 nonn,base
%O A371463 1,2
%A A371463 _Stefano Spezia_, Mar 24 2024