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I created this puzzle myself. Find the next number in this sequence and explain:

184275,
8292375,
3108105,
54729675,
147349125,
1587160575,
24135786675,
20906353125,
214266677625,
1676096296875,
9146402236125,
1188789606687375,
14837043862265625,
1268003106995625,
6561917002265625,
8610547490372953125,
30045013821087890625, 28918096701384515625,
928812978295467890625,
84135026523693427734375,
31040254903911427001953125,
38040322494031410287109375,
14178173111759846677863375,
392957986987929699059600830078125,
3481003119670913301423504641336001258544921875,
7400986580290704788541460659891195543870408269175363049221038818359375

Hint:

This is an unusual group of numbers.

Hint (this might make it too easy):

The finished sequence has length 27. What 27 unusual groups exist?

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  • $\begingroup$ Welcome to PSE (Puzzling Stack Exchange)! $\endgroup$
    – Will.Octagon.Gibson
    Commented Jul 6 at 2:36
  • $\begingroup$ It might be too early for an hint. Please try to wait for 24 hours :) I think the tags are enough for a hint for now $\endgroup$
    – Benjamin Wang
    Commented Jul 6 at 13:39
  • $\begingroup$ I find that the numbers are all products of small primes. The largest prime factor in any of them is 73 (and that's the last one). I don't know if this is relevant. As for the hint, perhaps rot13(hahfhny nf va bqq?) (I hope not.) $\endgroup$
    – David G.
    Commented Jul 10 at 11:32
  • $\begingroup$ rot13 is not involved. $\endgroup$
    – Lucenaposition
    Commented Jul 10 at 11:37

1 Answer 1

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The next number is

18445431375

because

this is related to Sporadic Groups. Take the prime factorization of the orders of sporadic groups, then "increase" them to the next prime numbers, e.g. 2^4 × 3^2 × 5 × 11 turns into 3^4 × 5^2 × 7 × 13 (the first term in the sequence)

making the missing term in the sequence

The Tits Group, which is sometimes considered a sporadic group.

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