A242347 Number of decimal digits of A008559.

1, 2, 4, 10, 31, 100, 330, 1093, 3628, 12049, 40023, 132951, 441651, 1467130, 4873698, 16190071, 53782249, 178660761, 593498199, 1971558339, 6549375034, 21756552927, 72273704413, 240088049208, 797555235908, 2649421145384, 8801186538037, 29236908829047, 97122908846869, 322635319555596

Offset

1,2

Comments

a(n+1)/a(n) is approximately log_2(10) = A020862. - André Engels, Apr 01 2021

Links

Yi Yang, Table of n, a(n) for n = 1..602

Code Golf StackExchange, Length of Binary as Base 10 [OEIS A242347], coding challenge started Oct 28 2022.

Yi Yang, Binary as Decimal and to Binary again (in Chinese).

Formula

a(n) = A055642(A008559(n)). - Michel Marcus, May 11 2014

Example

a(3) = 4 because 1010 has 4 decimal digits.

Prog

(Python)
A242347_list, l = [1], 2
for _ in range(10):
    l = int(bin(l)[2:])
    A242347_list.append(len(str(l))) # Chai Wah Wu, Dec 26 2014
(Python)
from itertools import islice
from gmpy2 import digits, mpz, bit_length
def agen(): # generator of terms
    an = 2
    yield 1
    while True:
        yield bit_length(an)
        an = mpz(digits(an, 2))
print(list(islice(agen(), 18))) # Michael S. Branicky, Jan 08 2026
(PARI) a242347(n) = {my (k=2, d=digits); while(n--, k=fromdigits(d(k, 2))); #d(k)} \\ Hugo Pfoertner, Nov 04 2022

Crossrefs

Cf. A008559, A055642, A020862.

Sequence in context: A001647 A007177 A328815 * A138415 A005268 A243931

Adjacent sequences: A242344 A242345 A242346 * A242348 A242349 A242350

Keyword

nonn,base

Author

J. Lowell, May 11 2014

Extensions

a(1), a(18)-a(20) from Chai Wah Wu, Dec 26 2014

a(21)-a(23) from Michael S. Branicky, Jan 08 2026

a(24) onward from Yi Yang, Apr 14 2026

Status

approved