

A299732


a(n) has exactly (a(n)  n) / 2 partitions with exactly (a(n)  n) / 2 prime parts.


2



2, 5, 8, 13, 20, 29, 42, 57, 78, 109, 148, 197, 264, 347, 454, 595, 770, 989, 1272, 1619, 2054, 2601, 3268, 4087, 5108, 6347, 7860, 9713, 11948, 14653, 17944, 21881, 26614, 32311, 39102, 47211, 56910, 68397, 82038, 98237, 117354, 139923, 166580, 197877, 234672
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OFFSET

0,1


COMMENTS

If B={b(n)} is the complement of A299731 then no number exists that has exactly b(n) partitions that have exactly b(n) prime parts, so this sequence lists only those numbers that can have the equality property.
Up to a(44) = 234672 (currently, the last term), except for 2,5,8, and 29, every term is the sum of distinct previous terms. Will this be true for all new terms?


LINKS



FORMULA



EXAMPLE

For n = 3: A299731(3) = 5. a(3) = 2*5 + 3 = 13. The five partitions of 13 that have exactly five prime parts are: (5,2,2,2,2), (3,3,3,2,2), (3,3,2,2,2,1), (3,2,2,2,2,1,1), and (2,2,2,2,2,1,1,1), so a(3) = 13.


PROG

(Python) # See Stauduhar link.


CROSSREFS



KEYWORD

nonn,changed


AUTHOR



STATUS

approved



