A379268 Numbers with only digits "1" and two digits "0".

100, 1001, 1010, 1100, 10011, 10101, 10110, 11001, 11010, 11100, 100111, 101011, 101101, 101110, 110011, 110101, 110110, 111001, 111010, 111100, 1001111, 1010111, 1011011, 1011101, 1011110, 1100111, 1101011, 1101101, 1101110, 1110011, 1110101, 1110110, 1111001

Offset: 1

Author

Chai Wah Wu, Dec 19 2024

Keywords

• nonn
• base

Comments

Binary representation of A379267.

Numbers in A007088 with two 0 digits.

Crossrefs

Cf. A007088, A379267, A023416, A357773.

Programs

Mathematica

Select[Range[10^7],Count[IntegerDigits[#],0]==2&&Max[IntegerDigits[#]]==1&] (* James C. McMahon, Dec 20 2024 *)

Python

from math import isqrt, comb
from sympy import integer_nthroot
def A379268(n):
    a = (m:=integer_nthroot(6*n, 3)[0])+(n>comb(m+2,3))+2
    b = isqrt((j:=comb(a,3)-n+1)<<3)+1>>1
    c = j-comb((r:=isqrt(w:=j<<1))+(w>r*(r+1)),2)-1
    return (10**a-1)//9-10**b-10**c

Formula

a(n) = A007088(A379267(n)).