OFFSET
1,2
COMMENTS
Equivalently, numbers whose digits have the coefficient of variation (or relative population standard deviation) equal to 1.
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
LINKS
EXAMPLE
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.
MAPLE
filter:= proc(x) local F, n, mu, i;
F:= convert(x, base, 10);
n:= nops(F);
mu:= convert(F, `+`)/n;
evalb(2*mu^2 = add(F[i]^2, i=1..n)/n)
end proc:
select(filter, [$0..10000]); # Robert Israel, Mar 24 2024
MATHEMATICA
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[#]&]
PROG
(Python)
from itertools import count, islice
def A371462_gen(startvalue=0): # generator of terms >= startvalue
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)))
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Stefano Spezia, Mar 24 2024
STATUS
approved