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

1,1

Comments

Binary representation of A379269.

Numbers in A007088 with three 0 digits.

Links

Table of n, a(n) for n=1..31.

Formula

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

Mathematica

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

Prog

(Python)
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])-(n<comb(m+2, 3))+2, 3)<<1))-((r<<2)<=(k<<2)*(k+1)+1)
def A333516(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

Crossrefs

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

Sequence in context: A017271 A017511 A326639 * A017643 A161770 A004632

Adjacent sequences: A379267 A379268 A379269 * A379272 A379273 A379274

Keyword

nonn,base

Author

Chai Wah Wu, Dec 19 2024

Status

approved