Sequences Of Mystery

[Leroy Quet]

Okay, I will put you all out of your misery and
reveal the solutions.

(See below quoted original message for
solutions.)


--- Leroy Quet <q1qq2qqq3qqqq at yahoo.com> wrote:

> I actually hate those "guess the rule that
> generated the sequence" puzzles, since, for one
> thing, there are an infinite number of rules
> and
> infinite sequences that fit any finite list of
> integers making up the first terms of the
> infinite sequence.
> 
> But I have been on the look-out anyway for any
> sequences of mine that would make a good puzzle
> of the sort.
> 
> And yesterday I actually came up with two
> sequences I think would make a good puzzle.
> (I am rather surprised that at least one of
> these
> sequences is not in the EIS yet.)
> 
> So before I submit these sequences to the OEIS
> I
> thought I would pose them here as a puzzle for
> those of you that, unlike me, don't hate these
> types of puzzles.
> 
> Sequence 1:
> 
>
0,1,1,1,1,2,1,0,0,2,1,2,1,2,2,1,1,2,1,2,2,2,1,2,0,2,1,2,1,3,...
> (Probably not too hard.)
> 
> 
> Sequence 2:
> 
> 0,1,1,3,1,5,1,7,4,7,1,11,1,9,7,15,1,17,1,19,
> 9,13,1,23,6,15,13,25,1,26,...
> (A bit harder.)
> 
> 
> Both sequences have offset 1.
> 
> And a hint for both sequences. For both
> sequences
> a(p) = 1, where p = any prime.


Sequence 1 is A136176.

Sequence 2 is A136180.


Thanks,
Leroy Quet




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