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phil1882

erdos decrepency conjecture

Question

heres an alternate version that i came up with,

place the digits 1-n where n is 4 such that no consecutive digit of any step value, starting at step value, repeats.

here's an example where n is 2.

0 1 0 2 1 0 2 1 2   0   1   ?   

1 2 3 4 5 6 7 8 9 10 11 12

here starting from 1 and going a step of 1, there are no repeats. starting from 2 and going a step of 2, no repeats, and so on. However there is no way to get 12 without repeating.

your task is to find the max value for 4.

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since it been a couple weeks without even a guess, I'll go ahead and post my answer and see if anyone can do better. i get 59.

0 1 0 2 0 3 0 1 0   3   0   2   0   1   0   3   0   1   0   2   0   1   0   4  0   1   0   2   0   3   0    1   0   3   0   2   0   1  0   4   0   1   0   2   0   1   0    3   0   1  

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 

0    2   0   1   0   4   0   1   0   ?

51 52 53 54 55 56 57 58 59 60

 

Edited by phil1882

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I think the example in the OP has a mistake in it?

Anyways, here's a length 120 sequence.

Spoiler

01020103010201040102010301020120210401030104010201040103010403210302412012342102310401202102010301242102312431303143014

 

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