A294023 -id:A294023 - cp's OEIS frontend

A294022 Sum of the differences of the larger and smaller parts in the partitions of n into two parts with the larger part prime.

0, 0, 1, 2, 1, 4, 3, 8, 6, 4, 3, 12, 10, 20, 18, 16, 14, 28, 25, 40, 36, 32, 29, 48, 44, 40, 37, 34, 31, 56, 52, 78, 73, 68, 64, 60, 56, 88, 84, 80, 76, 112, 107, 144, 138, 132, 127, 168, 162, 156, 150, 144, 138, 184, 177, 170, 163, 156, 150, 202, 195, 248

Offset: 1

Wesley Ivan Hurt, Oct 21 2017

Sum of the slopes of the tangent lines along the left side of the parabola b(x) = n*x-x^2 such that n-x is prime for x in 0 < x <= floor(n/2). For example, d/dx n*x-x^2 = n-2x. So for a(12), the integer values of x which make 12-x prime are x=1,5 and so a(12) = 12-2*1 + 12-2*5 = 10 + 2 = 12. - Wesley Ivan Hurt, Mar 24 2018

			There are two ways to partition n = 9 into a prime and a smaller positive integer: 7 + 2 and 5 + 4. So a(9) = (7 - 2) + (5 - 4) = 6. - _Michael B. Porter_, Mar 26 2018

Robert G. Wilson v, Table of n, a(n) for n = 1..1000
Index entries for sequences related to partitions

Cf. A010051, A294023.

Table[Sum[(n - 2 i) (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[n/2]}], {n, 60}]

a(n) = sum(i=1, n\2, (n - 2*i)*isprime(n-i)); \\ Michel Marcus, Mar 24 2018

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

cp's OEIS Frontend

A294022 Sum of the differences of the larger and smaller parts in the partitions of n into two parts with the larger part prime.

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