A239238 a(n) = |{0 <= k < n: q(n+k*(k+1)/2) + 1 is prime}|, where q(.) is the strict partition function given by A000009.
1, 2, 3, 2, 3, 1, 4, 5, 2, 4, 5, 4, 4, 4, 2, 4, 3, 6, 3, 1, 3, 5, 5, 5, 2, 9, 8, 7, 5, 3, 3, 4, 3, 7, 4, 8, 6, 2, 6, 6, 5, 2, 5, 5, 3, 3, 4, 4, 7, 7, 8, 5, 5, 4, 8, 6, 3, 4, 3, 5, 11, 2, 2, 4, 6, 6, 5, 5, 4, 4, 5, 6, 6, 8, 4, 9, 4, 6, 4, 3
Offset: 1
Keywords
Examples
a(6) = 1 since q(6+0*1/2) + 1 = q(6) + 1 = 5 is prime. a(20) = 1 since q(20+8*9/2) + 1 = q(56) + 1 = 7109 is prime. a(104) = 1 since q(104+15*16/2) + 1 = q(224) + 1 = 1997357057 is prime. a(219) = 1 since q(219+65*66/2) + 1 = q(2364) + 1 = 111369933847869807268722580000364711 is prime. a(1417) > 0 since q(1417+1347*1348/2) + 1 = q(909295) + 1 is prime.
Links
- Zhi-Wei Sun, Table of n, a(n) for n = 1..600
Programs
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Mathematica
q[n_]:=PartitionsQ[n] a[n_]:=Sum[If[PrimeQ[q[n+k(k+1)/2]+1],1,0],{k,0,n-1}] Table[a[n],{n,1,80}]
Comments