A364606 Numbers k such that the average digit of 2^k is an integer.

0, 1, 2, 3, 6, 13, 16, 26, 46, 51, 56, 73, 122, 141, 166, 313, 383

Offset

1,3

Links

Table of n, a(n) for n=1..17.

Formula

{ k : A001370(k) mod A034887(k) = 0 }.

Example

2^26 = 67108864 is an 8-digit number; its average digit is (6+7+1+0+8+8+6+4)/8 = 40/8 = 5, an integer, so 26 is a term.

Maple

q:= n-> (l-> irem(add(i, i=l), nops(l))=0)(convert(2^n, base, 10)):
select(q, [$0..400])[];  # Alois P. Heinz, Jul 29 2023

Mathematica

Select[Range[0, 2^12], IntegerQ@ Mean@ IntegerDigits[2^#] &] (* Michael De Vlieger, Jul 29 2023 *)

Prog

(PARI) isok(k) = my(d=digits(2^k)); !(vecsum(d) % #d); \\ Michel Marcus, Jul 29 2023
(Python)
from itertools import count, islice
from gmpy2 import mpz, digits
def A364606_gen(startvalue=0): # generator of terms >= startvalue
    m = mpz(1)<<max(startvalue, 0)
    for k in count(max(startvalue, 0)):
        s = digits(m)
        if not sum(int(d) for d in s) % len(s):
            yield k
        m <<= 1
A364606_list = list(islice(A364606_gen(), 10)) # Chai Wah Wu, Jul 31 2023

Crossrefs

Cf. A000079, A001370, A034887, A061383.

Sequence in context: A054049 A276690 A175281 * A244790 A111503 A239326

Adjacent sequences: A364603 A364604 A364605 * A364607 A364608 A364609

Keyword

nonn,base

Author

Jon E. Schoenfield, Jul 29 2023

Status

approved