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

1,1

Comments

Binary representation of A379267.

Numbers in A007088 with two 0 digits.

Links

Table of n, a(n) for n=1..33.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A007088, A379267, A023416, A357773.

Sequence in context: A173485 A173484 A136387 * A001737 A266838 A267127

Adjacent sequences: A379265 A379266 A379267 * A379269 A379270 A379273

Keyword

nonn,base

Author

Chai Wah Wu, Dec 19 2024

Status

approved