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[d(i)d(i+k),i=1,n-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

1,2

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}.

Links

Table of n, a(n) for n=1..10.

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

Example

For the sequence d=112102 we get Sum[d(i)d(i+k),i=1,n-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.

Crossrefs

Cf. A053006, A117549.

Sequence in context: A342792 A111300 A215761 * A175135 A244314 A014489

Adjacent sequences: A117545 A117546 A117547 * A117549 A117550 A117551

Keyword

nonn,more

Author

John W. Layman, Mar 28 2006

Status

approved