A038445 Sums of 3 distinct powers of 10.

111, 1011, 1101, 1110, 10011, 10101, 10110, 11001, 11010, 11100, 100011, 100101, 100110, 101001, 101010, 101100, 110001, 110010, 110100, 111000, 1000011, 1000101, 1000110, 1001001, 1001010, 1001100, 1010001, 1010010, 1010100, 1011000, 1100001, 1100010, 1100100

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A011557.

Cf. A038444, A038446, A038447, A038448, A038449, A038450, A038451, A038452, A038453, A038454.

Programs

Mathematica

Sort[Plus @@@ Subsets[10^Range[0, 6], {3}]] (* Amiram Eldar, Jul 12 2022 *)

Python

from math import isqrt, comb
from sympy import integer_nthroot
def A038445(n): return 10**((r:=n-1-comb((m:=integer_nthroot(6*n,3)[0])+(t:=(n>comb(m+2,3)))+1,3))-comb((k:=isqrt(b:=r+1<<1))+(b>k*(k+1)),2))+10**((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1))+10**(m+t+1) # Chai Wah Wu, Mar 10 2025