Sequences Of Mystery

[Leroy Quet]

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.

Thanks,
Leroy Quet




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