We are all familiar with the Fibonacci sequence:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765However, instead of, f(n) = f(n-1) + f(n-2) we'll be taking digital sum of the previous 2 entries.
The sequence should still start with 0, 1, after that the differences are rapidly apparent. This list is 0-indexed, you may use 1-indexed as well, state which you used.
f(0) = 0f(1) = 1f(2) = 1 # 0 + 1f(3) = 2 # 1 + 1f(4) = 3 # 1 + 2f(5) = 5 # 2 + 3f(6) = 8 # 3 + 5f(7) = 13 # 8 + 5f(8) = 12 # 8 + 1 + 3f(9) = 7 # 1 + 3 + 1 + 2f(10) = 10 # 1 + 2 + 7f(11) = 8 # 7 + 1 + 0f(12) = 9 # 1 + 0 + 8f(13) = 17 # 8 + 9f(14) = 17 # 9 + 1 + 7f(15) = 16 # 1 + 7 + 1 + 7f(16) = 15 # 1 + 7 + 1 + 6f(17) = 13 # 1 + 6 + 1 + 5f(18) = 10 # 1 + 5 + 1 + 3f(19) = 5 # 1 + 3 + 1 + 0f(20) = 6 # 1 + 0 + 5f(21) = 11 # 5 + 6f(22) = 8 # 6 + 1 + 1f(23) = 10 # 1 + 1 + 8f(24) = 9 # 8 + 1 + 0f(25) = 10 # 1 + 0 + 9f(26) = 10 # 9 + 1 + 0f(27) = 2 # 1 + 0 + 1 + 0(After this point it repeats at the 3rd term, 0-indexed)Note: I didn't notice the repetition until I posted the challenge itself, and here I was thinking it'd be impossible to write another novel Fibonacci challenge.
Your task is, given a number n, output the nth digit of this sequence.
First 3 digits: [0,1,1],
24-digit repeated pattern: [2,3,5,8,13,12,7,10,8,9,17,17,16,15,13,10,5,6,11,8,10,9,10,10]
Hint: You may be able to exploit this repetition to your advantage.
This is code-golf, lowest byte-count is the winner.
BONUS: If you use the repetition in your answer, I will award the lowest byte-count answer that takes advantage of the repetition in the sequence a bounty of 100 points. This should be submitted as part of your original answer, after your original answer. See this post as an example of what I am talking about: https://codegolf.stackexchange.com/a/108972/59376
To qualify for this bonus your code must run in constant time (O(1)) with an explanation.
Bonus Winner: Dennis https://codegolf.stackexchange.com/a/108967/59376< Dennis won.
Most Unique Implementation: https://codegolf.stackexchange.com/a/108970/59376
(Also will receive 100 points, finalized after correct answer is chosen)
