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A302480 Number of partitions of n into two parts with the smaller part nonprime and the larger part prime. 1
0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 1, 2, 2, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 3, 4, 1, 4, 0, 4, 3, 3, 1, 4, 1, 4, 3, 5, 2, 5, 1, 5, 2, 6, 3, 6, 2, 6, 4, 7, 3, 6, 1, 6, 5, 6, 2, 7, 1, 7, 6, 7, 3, 8, 3, 8, 5, 8, 4, 9, 2, 9, 6, 9, 5, 9, 2, 9, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,17

LINKS

Table of n, a(n) for n=1..86.

Index entries for sequences related to partitions

FORMULA

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

EXAMPLE

a(17) = 2; 17 = 13+4 = 11+6, smaller parts are nonprimes larger are prime.

MATHEMATICA

Table[Sum[(PrimePi[n - i] - PrimePi[n - i - 1]) (1 - (PrimePi[i] - PrimePi[i - 1])), {i, Floor[n/2]}], {n, 100}]

PROG

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

CROSSREFS

Cf. A010051, A302481.

Sequence in context: A210868 A176853 A261787 * A329656 A000374 A256757

Adjacent sequences:  A302477 A302478 A302479 * A302481 A302482 A302483

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Apr 08 2018

STATUS

approved

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Last modified April 7 13:32 EDT 2020. Contains 333305 sequences. (Running on oeis4.)