This is a simple number sequence puzzle, you are given 6 related number sequences, observe them, find the pattern; Your task is to give the first sixteen terms in the seventh sequence.

$$1d5, 2d3, 1d13, 1d21, 3d11, 1d57, 1d93, 19d7, 41d5, 1d397, 23d27, 1d1041, 281d5, 31d87, 1d4413, 1d7141$$

$$2d3, 1d9, 3d5, 7d3, 1d45, 1d73, 5d23, 1d193, 1d313, 127d3, 137d5, 19d69, 269d7, 1d3481, 313d17, 53d171$$

$$1d9, 3d3, 1d21, 1d33, 7d7, 5d17, 1d145, 59d3, 1d381, 103d5, 5d199, 1d1617, 17d153, 353d11, 149d45, 1109d9$$

$$1d13, 2d7, 5d5, 1d45, 19d3, 1d121, 11d17, 5d63, 37d13, 1d837, 113d11, 1d2193, 71d49, 359d15, 1549d5, 103d145$$

$$5d3, 1d21, 7d5, 2d31, 1d105, 17d9, 23d11, 1d445, 19d37, 73d15, 7d269, 139d21, 1237d3, 1d8005, 127d101, 131d159$$

$$5d5, 2d15, 1d61, 1d93, 13d11, 5d49, 29d13, 41d15, 59d17, 1d1717, 139d19, 173d25, 1213d5, 23d511, 1361d13, 3083d9$$

The numbers are expressed as dice averages. The accepted answer is expected to express the sequence in dice averages in the same format as the sequences above.


1 Answer 1


So, every number sequence is

a fibonacci sequence expressed in dice averages, meaning that 3d5 is the average score of throwing 3 dices that range from 1 to 5, so 3d5 = 9.

And every sequence starts with

subsequent terms of the original fibonacci sequence + 2. Meaning 1,2,3,5,8,13 turns into 3,4,5,7,10,15. So the 7th sequence starts with 21 -> 23. Also, the second term is the first term + 1. Therefore:

23, 24, 47, 71, 118, 189, 307, 496, 803, 1299, 2102, 3401, 5503, 8904, 14407, 23311

But it also needs to be translated into dice averages. Finally:

$$1d45, 3d15, 1d93, 1d141, 59d3, 7d53, 1d613, 31d31, 73d21, 433d5, 1051d3, 179d37, 1d11006, 56d335, 1d28813, 1d46621$$

I also should mention that the format for a number N = ndm is: you do prime factorization of N, and if it's a prime, n = 1. If it's not prime, n = biggest prime of the factorization. Then comes the "d", and last m = the number that makes the calculation correct.


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