A379269 -id:A379269 - cp's OEIS frontend

A379270 Numbers with only digits "1" and three digits "0".

1000, 10001, 10010, 10100, 11000, 100011, 100101, 100110, 101001, 101010, 101100, 110001, 110010, 110100, 111000, 1000111, 1001011, 1001101, 1001110, 1010011, 1010101, 1010110, 1011001, 1011010, 1011100, 1100011, 1100101, 1100110, 1101001, 1101010, 1101100

Offset: 1

Chai Wah Wu, Dec 19 2024

Binary representation of A379269.

Numbers in A007088 with three 0 digits.

Cf. A007088, A379269, A023416, A056557, A333516, A360010, A360573.

Select[Range[10^7],Count[IntegerDigits[#],0]==3&&Max[IntegerDigits[#]]==1&] (* James C. McMahon, Dec 20 2024 *)

from math import isqrt, comb
from sympy import integer_nthroot
def A056557(n): return (k:=isqrt(r:=n+1-comb((m:=integer_nthroot(6*(n+1), 3)[0])-(nA333516(n): return (r:=n-1-comb((m:=integer_nthroot(6*n, 3)[0])+(n>comb(m+2, 3))+1, 3))-comb((k:=isqrt(m:=r+1<<1))+(m>k*(k+1)), 2)+1
def A360010(n): return (m:=integer_nthroot(6*n, 3)[0])+(n>comb(m+2, 3))
def A379270(n):
    a = (a2:=integer_nthroot(24*n, 4)[0])+(n>comb(a2+2, 4))+2
    j = comb(a,4)-n
    b, c, d = A360010(j+1)+1, A056557(j)+1, A333516(j+1)-1
    return (10**a-1)//9-10**b-10**c-10**d

a(n) = A007088(A379269(n)).

cp's OEIS Frontend

A379270 Numbers with only digits "1" and three digits "0".

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