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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 FORMULA a(n) = Sum_{i=1..floor(n/2)} A010051(i) * (1 - A010051(n-i)). 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)*(1-isprime(n-i))); \\ 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

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)