OFFSET
0,7
COMMENTS
EXAMPLE
The a(2) = 1 through a(17) = 8 prime numbers:
2 3 5 . 17 11 19 . 257 131 73 137 97 521 4099 1031
7 13 67 41 71 263 2053 523
37 23 43 139 1033 269
29 83 193 163
53 47 149
31 101
89
79
The a(2) = 1 through a(11) = 3 strict partitions:
(2) (2,1) (3,1) . (5,1) (4,2,1) (4,3,1) . (9,1) (6,4,1)
(3,2,1) (5,2,1) (6,3,1) (8,2,1)
(7,2,1) (5,3,2,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&PrimeQ[Total[2^#]/2]&]], {n, 0, 30}]
CROSSREFS
For all positive integers (not just prime) we get A000009.
Number of prime numbers p with A029931(p) = n.
Number of times n appears in A372429.
Number of rows of A372471 with sum n.
These (strict) partitions have Heinz numbers A372851.
A014499 lists binary indices of prime numbers.
A048793 lists binary indices:
- length A000120
- min A001511
- sum A029931
- max A070939
- reverse A272020
A096111 gives product of binary indices.
A372689 lists numbers whose binary indices sum to a prime.
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 15 2024
STATUS
approved