A038465 Sums of 3 distinct powers of 3.

13, 31, 37, 39, 85, 91, 93, 109, 111, 117, 247, 253, 255, 271, 273, 279, 325, 327, 333, 351, 733, 739, 741, 757, 759, 765, 811, 813, 819, 837, 973, 975, 981, 999, 1053, 2191, 2197, 2199, 2215, 2217, 2223, 2269, 2271, 2277, 2295, 2431, 2433, 2439, 2457, 2511, 2917

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

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

Crossrefs

Base 3 interpretation of A038445.

Cf. A000244, A038464, A038466, A038467, A038468, A038469.

Programs

Mathematica

Total/@Subsets[3^Range[0,10],{3}]//Union (* Harvey P. Dale, Jul 10 2017 *)

Python

from math import comb, isqrt
from sympy import integer_nthroot
def A038465(n): return 3**((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))+3**((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1))+3**(m+t+1) # Chai Wah Wu, Apr 04 2025

Extensions

Offset corrected by Amiram Eldar, Jul 13 2022