A038471 Sums of 3 distinct powers of 4.

21, 69, 81, 84, 261, 273, 276, 321, 324, 336, 1029, 1041, 1044, 1089, 1092, 1104, 1281, 1284, 1296, 1344, 4101, 4113, 4116, 4161, 4164, 4176, 4353, 4356, 4368, 4416, 5121, 5124, 5136, 5184, 5376, 16389, 16401, 16404, 16449, 16452, 16464, 16641, 16644, 16656, 16704

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

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

Crossrefs

Base 4 interpretation of A038445.

Cf. A000302, A038470, A038472, A038473.

Programs

Mathematica

Union[Total/@Subsets[4^Range[0,10],{3}]] (* Harvey P. Dale, Oct 20 2012 *)

Python

from math import isqrt, comb
from sympy import integer_nthroot
def A038471(n): return (1<<((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)<<1))+(1<<((a:=isqrt(s:=n-comb(m-(t^1)+2,3)<<1))+((s<<2)>(a<<2)*(a+1)+1)<<1))+(1<<(m+t+1<<1)) # Chai Wah Wu, Apr 04 2025

Extensions

Offset corrected by Amiram Eldar, Jul 13 2022