OFFSET
0,8
COMMENTS
It appears that the only 0 in this sequence is a(16).
FORMULA
EXAMPLE
n = 0, a(n) = 1, 2^n = 1 - solution is 1;
n = 1, a(n) = 1, 2^n = 2 - solution is 2;
n = 2, a(n) = 1, 2^n = 4 - solution is 4;
n = 3, a(n) = 1, 2^n = 8 - solution is 8;
n = 4, a(n) = 1, 2^n = 16 - solution is 1;
n = 5, a(n) = 1, 2^n = 32 - solution is 2;
n = 6, a(n) = 1, 2^n = 64 - solution is 4;
n = 7, a(n) = 3, 2^n = 128 - solutions are 1,2,8;
n = 14, a(n) = 3, 2^n = 16384 - solutions are 1,4,8;
n = 15, a(n) = 2, 2^n = 32768 - solutions are 2,8;
n = 16, a(n) = 0, 2^n = 65536 - no solutions.
MATHEMATICA
Array[Total@ DigitCount[2^#, 10, {1, 2, 4, 8}] &, 85, 0] (* Michael De Vlieger, Dec 31 2018 *)
PROG
(Python 3.7)
import re
results = []
start_n = 0
N = 100
current_num = int(pow(2, start_n-1)) # Calculate (n-1) power. Convert to integer for better precision
for n in range(start_n, N):
if n == 0:
current_num = 1
else:
current_num += current_num
count = 0
for test_str in ["1", "2", "4", "8"]:
count += len(re.findall(test_str, str(current_num)))
results.append(count)
print(results)
(PARI) a(n) = #select(x->((x==1) || (x==2) || (x==4) || (x==8)), digits(2^n)); \\ Michel Marcus, Dec 30 2018
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Gaitz Soponski, Dec 28 2018
STATUS
approved