A309759 Numbers that are sums of consecutive powers of 4.

1, 4, 5, 16, 20, 21, 64, 80, 84, 85, 256, 320, 336, 340, 341, 1024, 1280, 1344, 1360, 1364, 1365, 4096, 5120, 5376, 5440, 5456, 5460, 5461, 16384, 20480, 21504, 21760, 21824, 21840, 21844, 21845, 65536, 81920, 86016, 87040, 87296, 87360, 87376, 87380

Offset: 1

Author

Ilya Gutkovskiy, Aug 15 2019

Keywords

• nonn

Comments

Numbers of the form (4^i - 4^j)/3 with i > j.

Examples

			336 = 4^2 + 4^3 + 4^4, so 336 is in the sequence.
+------+--------+
| a(n) | base 4*|
+------+--------+
|   1  |     1  |
|   4  |    10  |
|   5  |    11  |
|  16  |   100  |
|  20  |   110  |
|  21  |   111  |
|  64  |  1000  |
|  80  |  1100  |
|  84  |  1110  |
|  85  |  1111  |
+------+--------+
* - a(n) written in base 4.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000302, A000695, A023758, A038470, A309758, A309761.

Programs

Mathematica

Module[{nn=10,k},k=4^Range[0,nn];Table[Accumulate[Reverse[Take[k,n]]],{n,nn}]]//Flatten (* Harvey P. Dale, May 29 2021 *)

Python

from math import isqrt
def A309759(n): return ((1<<((m:=isqrt(n<<3)+1>>1)<<1))-(1<Chai Wah Wu, Apr 04 2025