A309758 Numbers that are sums of consecutive powers of 3.

1, 3, 4, 9, 12, 13, 27, 36, 39, 40, 81, 108, 117, 120, 121, 243, 324, 351, 360, 363, 364, 729, 972, 1053, 1080, 1089, 1092, 1093, 2187, 2916, 3159, 3240, 3267, 3276, 3279, 3280, 6561, 8748, 9477, 9720, 9801, 9828, 9837, 9840, 9841, 19683, 26244, 28431

Offset: 1

Author

Ilya Gutkovskiy, Aug 15 2019

Keywords

• nonn

Comments

Numbers of the form (3^i - 3^j)/2 with i > j.

Examples

			1080 = 3^3 + 3^4 + 3^5 + 3^6, so 1080 is in the sequence.
+------+--------+
| a(n) | base 3*|
+------+--------+
|   1  |     1  |
|   3  |    10  |
|   4  |    11  |
|   9  |   100  |
|  12  |   110  |
|  13  |   111  |
|  27  |  1000  |
|  36  |  1100  |
|  39  |  1110  |
|  40  |  1111  |
+------+--------+
* - a(n) written in base 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000244, A005836, A023758, A038464, A309759, A309761.

Programs

Maple

[seq(seq((3^i-3^j)/2,j=i-1..0,-1),i=1..20)]; # Robert Israel, Aug 19 2019

Python

from math import isqrt
def A309758(n): return 3**(m:=isqrt(n<<3)+1>>1)-3**(m*(m+1)-(n<<1)>>1)>>1 # Chai Wah Wu, Apr 04 2025