# A simple number sequence puzzle

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.

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.