A379268 - OEIS

%I #12 Dec 20 2024 19:11:47

%S 100,1001,1010,1100,10011,10101,10110,11001,11010,11100,100111,101011,

%T 101101,101110,110011,110101,110110,111001,111010,111100,1001111,

%U 1010111,1011011,1011101,1011110,1100111,1101011,1101101,1101110,1110011,1110101,1110110,1111001

%N Numbers with only digits "1" and two digits "0".

%C Binary representation of A379267.

%C Numbers in A007088 with two 0 digits.

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

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

%o (Python)

%o from math import isqrt, comb

%o from sympy import integer_nthroot

%o def A379268(n):

%o     a = (m:=integer_nthroot(6*n, 3)[0])+(n>comb(m+2,3))+2

%o     b = isqrt((j:=comb(a,3)-n+1)<<3)+1>>1

%o     c = j-comb((r:=isqrt(w:=j<<1))+(w>r*(r+1)),2)-1

%o     return (10**a-1)//9-10**b-10**c

%Y Cf. A007088, A379267, A023416, A357773.

%K nonn,base

%O 1,1

%A _Chai Wah Wu_, Dec 19 2024