[seqfan] Re: new sequences needing more terms

[Hans Havermann]

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?