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 A235613 Number of ways to write n = k + m (0 < k <= m) with k and m terms of A235592. 7

%I #8 Jan 13 2014 01:11:43

%S 0,0,0,1,1,2,2,3,2,3,3,3,3,3,2,3,4,3,3,4,3,5,6,5,4,4,3,4,6,5,4,5,4,4,

%T 5,4,4,6,5,8,6,6,5,5,6,6,8,6,6,6,4,7,6,5,7,9,6,6,8,5,4,7,9,7,8,6,6,7,

%U 3,5,7,9,8,9,9,6,6,5,6,7,6,8,5,4,4,4,4,8,10,10,10,7,6,6,8,7,6,10,6,6

%N Number of ways to write n = k + m (0 < k <= m) with k and m terms of A235592.

%C Conjecture: a(n) > 0 for all n > 3.

%H Zhi-Wei Sun, <a href="/A235613/b235613.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4) = 1 since 4 = 2 + 2 with 2*(2+1) - prime(2) = 3 prime.

%e a(5) = 1 since 5 = 2 + 3 with 2*(2+1) - prime(2) = 3 and 3*(3+1) - prime(3) = 7 both prime.

%t p[n_]:=PrimeQ[n(n+1)-Prime[n]]

%t a[n_]:=Sum[If[p[k]&&p[n-k],1,0],{k,1,n/2}]

%t Table[a[n],{n,1,100}]

%Y Cf. A000040, A235592, A235614.

%K nonn

%O 1,6

%A _Zhi-Wei Sun_, Jan 12 2014

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Last modified December 7 01:11 EST 2023. Contains 367616 sequences. (Running on oeis4.)