# Mathematical Codebreaking

I've created a puzzle and dressed it up as a puzzle.

The following message has been intercepted. You suspect it begins with the words THE KEY TO THIS METHOD. Decipher the message and describe the cipher method.

UJIPLGEBIXBMICVKUKSETJGYXMHRAIY


If we take A1Z26 of both the cipher and UJIPLGEBIXBMICVKUKSETJGYXMHRAIY, we get:

20|08|05|11|05|25|20|15|20|08|09|19|13|05|20|08|15|04 21|10|09|16|12|07|05|02|09|24|02|13|09|03|22|11|21|11

After the 6th column, for some entries our top number is greater than our bottom number, so we will add 26 if that is the case.

20|08|05|11|05|25|20|15|20|08|09|19|13|05|20|08|15|04 21|10|09|16|12|33|31|28|35|24|28|39|35|29|22|11|21|11

So now we make the completely arbitrary case to

always add 26 to out bottom number after the 16th row.

So we change into

20|08|05|11|05|25|20|15|20|08|09|19|13|05|20|08|15|04 21|10|09|16|12|33|31|28|35|24|28|39|35|29|48|37|47|37

If we

subtract the bottom number from the top number

we get:

1, 2, 4, 5, 7, 8, 11, 13, 15, 16, 19, 20, 22, 24, 28, 29, 32, 33

which is

sequence A022559 in the OEIS, or the sum of exponents in the prime-power factorization in n!.

• This sequence is A022559 in OEIS. Jul 11, 2023 at 6:10
• Oh. Well. I'll just go ahead and accept this answer, then. If anyone wants extra credit, they can figure out how to discover the sequence without using OEIS. Jul 11, 2023 at 7:55