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

1,57

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

Links

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

Example

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

Crossrefs

Column k=1 of A254218.

Sequence in context: A326368 A197343 A289941 * A086501 A204241 A053115

Adjacent sequences: A254208 A254209 A254210 * A254212 A254213 A254214

Keyword

nonn,look,nice

Author

R. H. Hardin, Jan 26 2015

Status

approved