A254211 Number of length n 1..(1+2) arrays with no leading or trailing partial sum equal to a prime and no consecutive values equal.

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, 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, 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

Offset: 1

Author

R. H. Hardin, Jan 26 2015

Keywords

• nonn
• look
• nice

Comments

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

(i) u_i = 1,2 or 3,

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

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

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

Conjecture: There are infinitely many n > 0 with a(n) > 0. - Alois P. Heinz, Jan 27 2015

Examples

			All solutions for n=5:
..1
..3
..2
..3
..1
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1970

Crossrefs

Column k=1 of A254218.