Two number sequence puzzles

1. 123456, ?, 32407290, 128028806480
2. 122540, 577697, ?, ?

Both puzzles are from - https://free.ultimaiq.net/nse.htm

• Having only two numbers to figure out a specific sequence is pretty absurd. Commented Dec 20, 2023 at 11:16
• I beg to differ lol
– PDT
Commented Dec 20, 2023 at 12:21
• Well, even though your answer makes a lot of sense, I do think giving at least one more number to rule out possibilities could make the puzzle better. There's nothing non-logical in assuming this could be an arithmetic sequence and guessing 1032854, 1488011. Commented Dec 20, 2023 at 12:50

First one is

4081904

Because

it is just separating a number of the sequence into pairs (xx,xx,xx) e.g 123456 becomes 12,34,56 and then multiplying the pairs that are adjacent to each other to generate a number for the next number in the sequence. This is done in order of appearance of the pair of pairs in the number and once you generate the numbers you group them all together in that order which you generated them. So for example in 32407290 you get 32 x 40 which equals 1280 and 40 x 72 which gets 2880 and 72 x 90 which gets 6480 which when grouped together gets 128028806480. So 12x34 is 408 and 34x56 is 1904… then you get 4081904

Second one is

120145, 172201

Because

If we put a comma after every number generated starting from 12 and adding 13 then (+2) 15 then (+2)17 then (+2)19 then (+2)21 etc you get 12,25,40,57,76,97. Following this logic you get 97+23 or 120 then 120+25 which is 145 and then 145+27 which is 172 and then 172+29 which is 201 etc

Then

For each group of 6 adjacent digits, you group them together to form one number and so you eventually get 120145, 172201 as the 3rd and 4th term.

• Yeah, this is the right answer. You should try the upper one as well. Commented Dec 20, 2023 at 11:26