A117548 Values of n for which there exist d(1),...,d(n), each in {0,1,2} and an r in {1,2} such that Sum_{i=1..n-k} d(i)*d(i+k) == r (mod 3) for all k=0..n-1. (Such a sequence is called a very(3,r) sequence. See the link.).

1, 2, 5, 6, 7, 12, 14, 17, 20, 24

Offset: 1

Author

John W. Layman, Mar 28 2006

Keywords

• nonn
• more

Comments

Theorem. Let a be a very(3,r) sequence of length n, for r=1 or 2 and let z be a sequence of n-1 0's. Then az(2a) is a very(3,3-r) sequence of length 3n-1, where 2a denotes the sequence {2a(i) mod 3, i=1..n}.

Examples

			For the sequence d=112102 we get Sum_{i=1..n-k} d(i)*d(i+k) = {11,5,5,5,2,2} = {2,2,2,2,2,2} (mod 3) for k=0..5, so 6 is a term of the sequence.
		

Links

• John W. Layman, On A Generalization of Very Odd Sequences

Crossrefs

Cf. A053006, A117549.