A038470 Sums of 2 distinct powers of 4.

5, 17, 20, 65, 68, 80, 257, 260, 272, 320, 1025, 1028, 1040, 1088, 1280, 4097, 4100, 4112, 4160, 4352, 5120, 16385, 16388, 16400, 16448, 16640, 17408, 20480, 65537, 65540, 65552, 65600, 65792, 66560, 69632, 81920, 262145, 262148, 262160, 262208, 262400, 263168

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 A038444.

Cf. A000302, A038471, A038472, A038473.

Programs

Mathematica

Sort[Plus @@@ Subsets[4^Range[0, 9], {2}]] (* Amiram Eldar, Jul 13 2022 *)

Python

def aupto(limit):
  p = [4**i for i in range(limit//4+1) if 4**i < limit]
  p2 = set(a+b for i, a in enumerate(p) for b in p[i+1:] if a+b <= limit)
  return sorted(p2)
print(aupto(265000)) # Michael S. Branicky, May 17 2021

Python

from math import isqrt
def A038470(n): return (1<<(m:=isqrt(n<<3)+1&-2))+(1<<(n-1<<1)-((k:=m>>1)*(k-1))) # Chai Wah Wu, Apr 05 2025

Extensions

Offset corrected by Amiram Eldar, Jul 13 2022