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Number of length n 1..(1+2) arrays with no leading or trailing partial sum equal to a prime and no consecutive values equal.
3

%I #21 Jan 27 2015 17:45:42

%S 1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,18,456,2178,3376,2222,

%U 720,158,24,0,0,0,0,0,10,122,204,116,26,2,10,72,84,25,6,4,0,0,0,0,0

%N Number of length n 1..(1+2) arrays with no leading or trailing partial sum equal to a prime and no consecutive values equal.

%C These are vectors [u_1 ... u_n] such that

%C (i) u_i = 1,2 or 3,

%C (ii) u_i != u_{i+1},

%C (iii) Sum_{i=1..k} u_i != prime for k=1..n,

%C (iv) Sum_{i=k..n} u_i != prime for k=1..n.

%C Conjecture: There are infinitely many n > 0 with a(n) > 0. - _Alois P. Heinz_, Jan 27 2015

%H Alois P. Heinz, <a href="/A254211/b254211.txt">Table of n, a(n) for n = 1..1970</a>

%e All solutions for n=5:

%e ..1

%e ..3

%e ..2

%e ..3

%e ..1

%Y Column k=1 of A254218.

%K nonn,look,nice

%O 1,57

%A _R. H. Hardin_, Jan 26 2015