OFFSET
0,5
COMMENTS
EXAMPLE
The partition y = (4,3,1,1) has distinct parts {1,3,4}, which are the binary indices of 13, which is prime, so y is counted under a(9).
The a(2) = 1 through a(9) = 14 partitions:
(2) (21) (22) (221) (51) (331) (431) (3321)
(31) (311) (222) (421) (521) (4221)
(211) (2111) (321) (511) (2222) (4311)
(2211) (2221) (3221) (5211)
(3111) (3211) (3311) (22221)
(21111) (22111) (4211) (32211)
(31111) (5111) (33111)
(211111) (22211) (42111)
(32111) (51111)
(221111) (222111)
(311111) (321111)
(2111111) (2211111)
(3111111)
(21111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], PrimeQ[Total[2^(Union[#]-1)]]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 19 2024
STATUS
approved