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

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

Links

Table of n, a(n) for n=1..45.

Wikipedia, Coefficient of variation.

Wikipedia, Standard deviation.

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

Crossrefs

Cf. A371383, A371384, A371462, A371464.

Cf. A238619, A238620, A238658, A238660, A238662.

Sequence in context: A318957 A356064 A180055 * A346003 A164007 A101870

Adjacent sequences: A371460 A371461 A371462 * A371464 A371465 A371466

Keyword

nonn,base

Author

Stefano Spezia, Mar 24 2024

Status

approved