

A084360


Number of partitions of n into pair of parts whose difference is a prime.


0



0, 0, 0, 1, 1, 1, 2, 1, 3, 1, 3, 1, 4, 1, 5, 1, 5, 1, 6, 1, 7, 1, 7, 1, 8, 1, 8, 1, 8, 1, 9, 1, 10, 1, 10, 1, 10, 1, 11, 1, 11, 1, 12, 1, 13, 1, 13, 1, 14, 1, 14, 1, 14, 1, 15, 1, 15, 1, 15, 1, 16, 1, 17, 1, 17, 1, 17, 1, 18, 1, 18, 1, 19, 1, 20, 1, 20, 1, 20, 1, 21, 1, 21, 1, 22, 1, 22, 1, 22, 1
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OFFSET

1,7


COMMENTS

Order of set A = { (p,q): p+q = n, q>=p and qp is a prime}.
a(1) = a(2) = 0; for even n >= 4, a(n) = 1; for odd n >= 3, a(n) = pi(n1)  1, where pi(n) = A000720(n) is the prime counting function.  Wesley Ivan Hurt, Feb 01 2013


LINKS

Table of n, a(n) for n=1..90.


FORMULA

a(n) = ( pi(n1)2 )*( n mod 2 ) + 1 + floor(1/n)  floor(n/2)*floor(2/n).  Wesley Ivan Hurt, Feb 01 2013
a(n) = Sum_{i=1..floor(n/2)} A010051(n2i).  Wesley Ivan Hurt, Apr 10 2018


EXAMPLE

a(7) = 2 and the partitions are (1,6) and (2,5).


MATHEMATICA

a[1] = a[2] = 0; a[n_] := If[EvenQ[n], 1, PrimePi[n  1]  1]; Array[a, 90] (* JeanFrançois Alcover, Nov 24 2016, after Wesley Ivan Hurt *)


CROSSREFS

Cf. A000720, A010051.
Sequence in context: A306248 A327513 A327530 * A082460 A318573 A029227
Adjacent sequences: A084357 A084358 A084359 * A084361 A084362 A084363


KEYWORD

nonn,easy


AUTHOR

Amarnath Murthy, May 27 2003


EXTENSIONS

More terms from Michel ten Voorde, Jun 20 2003


STATUS

approved



