Hi everyone! do you know anything about this sequence?

[Martin Doina]

0, 2, 3, 6, 11, 11, 16, 21, 22, 48, 49, 56, 99, 108, 116, 222, 431, 552, 660,

1080, 3784, 4297, 6288, 6991, 14881, 15106, 34862, 67334, 104980,

120182, 129824, 152012, 162913, 185783, 213219, 215563, 289425, 371036,

386164, 412949, 681399

thanks

[White Board]

Would you kindly share the motivation or the background by which you got such a sequence? Without any clue, it's tough to find out its uniqueness!

--Rad

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[Siddhartha Mahajan]

Hi Martin,

I think this is

a(n) = floor(p(n)/200), for n >= 12,

where p(n) is the n-th Mersenne-prime exponent (p(12)=127).

So:
127 → 0,
521 → 2,
607 → 3,
1279 → 6,
2203 → 11,
2281 → 11,

Is this the construction? How did you come across this?
I got to Mersenne by looking at some of the stuff you have recently posted about and worked on. Was a fun puzzle, thanks!

Best,
Siddhartha