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A291708 Number of partitions of n into two prime parts or two nonprime parts. 0
0, 1, 0, 1, 2, 1, 2, 2, 2, 4, 1, 3, 3, 4, 3, 6, 2, 6, 4, 6, 4, 8, 3, 9, 5, 9, 4, 9, 5, 11, 7, 9, 7, 13, 6, 15, 7, 10, 9, 14, 8, 16, 10, 14, 10, 16, 9, 19, 11, 18, 10, 17, 11, 21, 13, 18, 12, 20, 13, 25, 15, 18, 15, 24, 14, 27, 15, 19, 17, 26, 16, 28, 18, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..74.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{i=1..floor(n/2)} [A010051(i) = A010051(n-i)], where [] is the Iverson bracket.

a(n) = floor(n/2) - A062602(n).

MATHEMATICA

Table[Sum[KroneckerDelta[(PrimePi[k] - PrimePi[k - 1]), (PrimePi[n - k] - PrimePi[n - 1 - k])], {k, Floor[n/2]}], {n, 80}]

CROSSREFS

Cf. A010051, A062602.

Sequence in context: A322141 A029170 A079526 * A163822 A029203 A159805

Adjacent sequences:  A291705 A291706 A291707 * A291709 A291710 A291711

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Oct 20 2017

STATUS

approved

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Last modified May 9 10:46 EDT 2021. Contains 343732 sequences. (Running on oeis4.)