

A302481


Number of partitions of n into two parts with the smaller part prime and the larger part nonprime.


2



0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 2, 2, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 4, 3, 6, 4, 6, 3, 5, 4, 5, 3, 7, 3, 7, 6, 7, 5, 8, 4, 7, 5, 7, 5, 9, 4, 8, 5, 9, 6, 9, 4, 8, 6, 9, 6, 10, 4, 9, 8, 10, 6, 11, 5, 11, 9, 10, 6, 11, 5, 10, 7, 11, 7, 12, 5, 12, 8, 11, 8
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OFFSET

1,11


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for sequences related to partitions


FORMULA

a(n) = Sum_{i=1..floor(n/2)} A010051(i) * (1  A010051(ni)).


EXAMPLE

a(11) = 3; 11 = 9+2 = 8+3 = 6+5, smaller parts are prime, larger nonprime.


MATHEMATICA

Table[Sum[(1  (PrimePi[n  i]  PrimePi[n  i  1])) (PrimePi[i]  PrimePi[i  1]), {i, Floor[n/2]}], {n, 100}]
Table[Count[Boole[PrimeQ[#]&/@IntegerPartitions[n, {2}]], _?(#=={0, 1}&)], {n, 90}] (* Harvey P. Dale, Jan 05 2020 *)


PROG

(PARI) a(n) = sum(i=1, n\2, isprime(i)*(1isprime(ni))); \\ Michel Marcus, Apr 09 2018


CROSSREFS

Cf. A010051, A302480.
Sequence in context: A085034 A119323 A102299 * A306542 A259652 A141070
Adjacent sequences: A302478 A302479 A302480 * A302482 A302483 A302484


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Apr 08 2018


STATUS

approved



