A256077 Repeat 2^d times the repunit A002275(d); d = 1, 2, 3...

1, 1, 11, 11, 11, 11, 111, 111, 111, 111, 111, 111, 111, 111, 1111, 1111, 1111, 1111, 1111, 1111, 1111, 1111, 1111, 1111, 1111, 1111, 1111, 1111, 1111, 1111, 11111, 11111, 11111, 11111, 11111, 11111, 11111, 11111, 11111, 11111, 11111, 11111

Offset: 1

Author

M. F. Hasler, Mar 21 2015

Keywords

• nonn

Comments

Yields the length of the n-th (nonempty) binary word (or word over any 2-letter alphabet, like A007931 or A032810 or A032834) in tally mark notation (A000042).

Links

• Felix Fröhlich, Table of n, a(n) for n = 1..10000

Programs

Mathematica

lim = 5; lst = Table[(10^n - 1)/9, {n, 0, lim}]; Reap@ For[i = 1, i <= lim, i++, Sow@ Table[lst[[i + 1]], {d, 2^i}]] // Flatten // Rest (* Michael De Vlieger, Apr 01 2015 *)

PARI

a(n)=10^#binary(n+1)\90

Python

def A256077(n): return (10**((n+1).bit_length()-1)-1)//9 # Chai Wah Wu, Nov 07 2024

Formula

a(n) = A002275(A000523(n+1)) = A032810(n)-A007931(n) = A032834(n)-A032810(n), etc.