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%I #21 Jan 22 2020 20:09:17
%S 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,
%T 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,
%U 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
%N Number of partitions of n into pair of parts whose difference is a prime.
%C Order of set A = { (p,q): p+q = n, q>=p and q-p is a prime}.
%C a(1) = a(2) = 0; for even n >= 4, a(n) = 1; for odd n >= 3, a(n) = pi(n-1) - 1, where pi(n) = A000720(n) is the prime counting function. - _Wesley Ivan Hurt_, Feb 01 2013
%H Antti Karttunen, <a href="/A084360/b084360.txt">Table of n, a(n) for n = 1..20000</a>
%F a(n) = ( pi(n-1)-2 )*( n mod 2 ) + 1 + floor(1/n) - floor(n/2)*floor(2/n). - _Wesley Ivan Hurt_, Feb 01 2013
%F a(n) = Sum_{i=1..floor(n/2)} A010051(n-2i). - _Wesley Ivan Hurt_, Apr 10 2018
%e a(7) = 2 and the partitions are (1,6) and (2,5).
%t a[1] = a[2] = 0; a[n_] := If[EvenQ[n], 1, PrimePi[n - 1] - 1]; Array[a, 90] (* _Jean-François Alcover_, Nov 24 2016, after _Wesley Ivan Hurt_ *)
%o (PARI) A084360(n) = if(n<=2,0,if(!(n%2),1,primepi(n-1)-1)); \\ _Antti Karttunen_, Jan 22 2020
%Y Cf. A000720, A010051, A082460.
%K nonn,easy
%O 1,7
%A _Amarnath Murthy_, May 27 2003
%E More terms from _Michel ten Voorde_, Jun 20 2003
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