# Do you know what's next?

'Predict' the next few (5 or 6) terms of this series.

1, 1, 1, 2, 3, 6, 7, 10, 11, 12, 17, ...?

Hint: Who is the 'prime' suspect in this mystery sequence?

14, 17, 27, 34, 55, 63. This is just OEIS A000837: Number of partitions of n into relatively prime parts.

Note: This answer was written when only the terms "1,1,1,2,3,6,7" were in the puzzle. The OP added more terms to the puzzle after this answer was written.

• That was not the intention. However, thank you for the answer. Can you think of something else ? – Mike Karter May 25 '19 at 16:22
• I do not agree that OP added more terms to make this "wrong". Rather, he added more terms to clarify the problem. This does not necessarily change the answer they had in mind. Never assume malice over err. – greenturtle3141 May 25 '19 at 19:48
• (Cont’d) … (4) When a question is too broad, the author is encouraged to edit it to narrow the scope; i.e., to rule out answer(s) other than the intended one.  This happens all the time.  It’s tough luck to stumble across a question that’s too broad, provide an answer that’s correct, and then be told that it’s not what the OP meant / wanted, but it happens all the time.  Please do not accuse the OP of singling you out or attacking you ‘‘for no legitimate reason’’. – Peregrine Rook May 25 '19 at 22:23
• @PeregrineRook Fair; answer edited. – Joseph Sible-Reinstate Monica May 25 '19 at 22:35

WARNING this answer is probably very wrong.

I am bad at wording things so I put a visual. It's like pascal's triangle but with subtraction.

The second line of the blue pascal's triangle shows

0, 0, 1, 1, 3, 1, 3, 1, 1, 5

Which may be a fractal-like series. Again i'll show you it, not knowing how to explain it:

• 0

• 0

• 1

• 1, 3, {1}, 3, 1

• 1, 5, {1, 3, 1, 3, 1}, 5, 1

• 1, 7, {1, 5, 1, 3, 1, 3, 1, 5, 1}, 7, 1

And somehow the zeroes get added back in after the infinite series.

So therefore the pattern of differences will be

0, 0, 1, 1, 3, 1, 3, 1, 1, 5, 1, 3, 1, 3, 1, 5, 1, 1, 7 etc.

And finally, by adding the differences back into the numbers, we get:

1, 1, 1, 2, 3, 6, 7, 10, 11, 12, 17, 18, 21, 22, 25, 26, 31, 32, 33, 40 etc.

YAYYY!!!!