A238405 a(n) = |{0 < k < n: prime(k) + pi(n-k) is a triangular number}|, where pi(.) is given by A000720.
0, 0, 2, 0, 1, 0, 1, 2, 3, 3, 2, 2, 1, 3, 3, 1, 2, 1, 2, 5, 3, 3, 4, 1, 2, 2, 3, 3, 1, 2, 3, 4, 5, 6, 5, 3, 2, 2, 3, 3, 2, 5, 5, 4, 3, 2, 4, 3, 2, 3, 3, 2, 4, 6, 4, 6, 9, 8, 6, 4, 3, 2, 3, 4, 5, 3, 5, 6, 5, 5, 1, 1, 3, 5, 4, 4, 9, 7, 6, 6, 4, 6, 3, 3, 5, 8, 8, 5, 4, 7, 8, 4, 5, 3, 2, 3, 4, 4, 4, 4
Offset: 1
Keywords
Examples
a(7) = 1 since 7 = 2 + 5 with prime(2) + pi(5) = 3 + 3 = 3*4/2. a(24) = 1 since 24 = 4 + 20 with prime(4) + pi(20) = 7 + 8 = 5*6/2. a(158) = 1 since 158 = 148 + 10 with prime(148) + pi(10) = 857 + 4 = 41*42/2.
Links
- Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
TQ[n_]:=IntegerQ[Sqrt[8n+1]] a[n_]:=Sum[If[TQ[Prime[k]+PrimePi[n-k]],1,0],{k,1,n-1}] Table[a[n],{n,1,100}]
Comments