cp's OEIS Frontend

A371462 Numbers such that the arithmetic mean of its digits is equal to the population standard deviation of its digits.

%I A371462 #21 Mar 31 2024 04:39:20
%S A371462 0,10,20,30,40,50,60,70,80,90,1001,1010,1014,1041,1049,1094,1100,1104,
%T A371462 1140,1401,1409,1410,1490,1904,1940,2002,2020,2028,2082,2200,2208,
%U A371462 2280,2802,2820,3003,3030,3300,4004,4011,4019,4040,4091,4101,4109,4110,4190,4400,4901,4910
%N A371462 Numbers such that the arithmetic mean of its digits is equal to the population standard deviation of its digits.
%C A371462 Equivalently, numbers whose digits have the coefficient of variation (or relative population standard deviation) equal to 1.
%C A371462 Any number obtained without leading zeros from a permutation of the digits of a given term of the sequence is also a term.
%C A371462 The concatenation of several copies of any term is a term. - _Robert Israel_, Mar 24 2024
%H A371462 Wikipedia, <a href="https://en.wikipedia.org/wiki/Coefficient_of_variation">Coefficient of variation</a>.
%H A371462 Wikipedia, <a href="https://en.wikipedia.org/wiki/Standard_deviation">Standard deviation</a>.
%e A371462 1014 is a term since the mean of the digits is (1 + 0 + 1 + 4)/4 = 3/2 and the standard deviation of the digits is sqrt(((1-3/2)^2 + (0-3/2)^2 + (1-3/2)^2 + (4-3/2)^2)/4) = sqrt((1/4 + 9/4 + 1/4 + 25/4)/4) = sqrt(9/4) = 3/2.
%p A371462 filter:= proc(x) local F,n,mu,i;
%p A371462   F:= convert(x,base,10);
%p A371462   n:= nops(F);
%p A371462   mu:= convert(F,`+`)/n;
%p A371462   evalb(2*mu^2 = add(F[i]^2,i=1..n)/n)
%p A371462 end proc:
%p A371462 select(filter, [$0..10000]); # _Robert Israel_, Mar 24 2024
%t A371462 DigStd[n_]:=If[n==0||IntegerLength[n]==1, 0, Sqrt[(IntegerLength[n]-1)/IntegerLength[n]]StandardDeviation[IntegerDigits[n]]]; Select[Range[0, 5000], Mean[IntegerDigits[#]]==DigStd[#]&]
%o A371462 (Python)
%o A371462 from itertools import count, islice
%o A371462 def A371462_gen(startvalue=0): # generator of terms >= startvalue
%o A371462     return filter(lambda n:sum(map(int,(s:=str(n))))**2<<1 == len(s)*sum(int(d)**2 for d in s), count(max(startvalue,0)))
%o A371462 A371462_list = list(islice(A371462_gen(),20)) # _Chai Wah Wu_, Mar 28 2024
%Y A371462 Cf. A371383, A371384, A371463, A371464.
%Y A371462 Cf. A238619, A238620, A238658, A238660, A238662.
%K A371462 nonn,base
%O A371462 1,2
%A A371462 _Stefano Spezia_, Mar 24 2024