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

0, 12, 21, 24, 36, 42, 48, 63, 84, 1122, 1212, 1221, 2112, 2121, 2211, 2244, 2424, 2442, 2556, 2565, 2655, 3366, 3447, 3474, 3636, 3663, 3744, 4224, 4242, 4347, 4374, 4422, 4437, 4473, 4488, 4734, 4743, 4848, 4884, 5256, 5265, 5526, 5562, 5625, 5652, 6255, 6336, 6363

Offset

1,2

Comments

Equivalently, numbers whose digits have the coefficient of variation (or relative population standard deviation) equal to 1/3.

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..48.

Wikipedia, Coefficient of variation.

Wikipedia, Standard deviation.

Example

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.

Mathematica

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[#]&]

Prog

(Python)
from itertools import count, islice
def A371464_gen(startvalue=0): # generator of terms >= startvalue
    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)))
A371464_list = list(islice(A371464_gen(), 20)) # Chai Wah Wu, Mar 30 2024

Crossrefs

Cf. A371383, A371384, A371462, A371463.

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

Sequence in context: A248378 A349649 A327297 * A199981 A274347 A316266

Adjacent sequences: A371461 A371462 A371463 * A371465 A371466 A371467

Keyword

nonn,base

Author

Stefano Spezia, Mar 24 2024

Status

approved