# [seqfan] Re: new sequences needing more terms

Hans Havermann gladhobo at teksavvy.com
Thu May 31 14:42:01 CEST 2012

```A212814
a(n) = number of integers k >= 7 such that A212813(k) = n.
1, 3, 11, 2632
...
The 11 numbers k for which A212813(k)=2 are 9, 11, 14, 20, 24, 27, 28,
40, 45, 48, 54

I don't know how a(4) was calculated but, empirically, it appears that
2632 is the sum of the number of prime partitions (A000607) of the
eleven numbers 8, 10, 13, 19, 23, 26, 27, 39, 44, 47, 53. I hesitate
turning this into a conjecture only because the 3 numbers k for which
A212813(k)=1 are 7, 10, 12 and the sum of the number of prime
partitions of the three numbers 6, 9, 11 is twelve, not eleven (the
extra partition being, I think, 2+2+2).

Assuming that a(5) is indeed the sum of the number of prime partitions
of the 2632 numbers in a(4) doesn't just imply that "the next term may
be very large" (as Neil comments) but that a(5) is essentially
incalculable, since it would include the number of prime partitions of
2*3^86093441-1. Is there even a way to approximate this?

```