# [seqfan] Question about Three Integers Whose Sum is 2^N

Andras andras at yahoo.com
Sun Feb 26 05:58:17 CET 2023

```Hello Sequence Fans,

I have three ratioed integers whose sum is 524288:

111493, 374949, 37846

If I delete the final digit from each binary string and add them up, I will always get a sum of exactly 2^N.

Does anyone happen to know the exact name of this phenomenon ?

0011011001110000101 + 1011011100010100101 + 0001001001111010110 == 524288 [2^19]
11011001110000101 + 11011100010100101 + 01001001111010110 == 262144 [2^18]
1011001110000101 + 1011100010100101 + 1001001111010110 == 131072 [2^17]
011001110000101 + 011100010100101 + 001001111010110 == 32768 [2^15]
1001110000101 + 1100010100101 + 1001111010110 == 16384 [2^14]
001110000101 + 100010100101 + 001111010110 == 4096 [2^12]
01110000101 + 00010100101 + 01111010110 == 2048 [2^11]
110000101 + 010100101 + 111010110  == 1024 [2^10]
10000101 + 10100101 + 11010110 == 512 [2^9]
0000101 + 0100101 + 1010110 == 128 [2^7]
000101 + 100101 + 010110 == 64 [2^6]
00101 + 00101 + 10110 == 32 [2^5]
0101 + 0101 + 0110 == 16 [2^4]
01 + 01 + 10 == 4 [2^2]
1 + 1 + 0 == 2 [2^1]

```