A117549 Values of n for which there exist d(1),...,d(n), each in {0,1,...,4} and an r in {1,...,4} such that Sum[d(i)d(i+k),i=1,n-k]=r (mod 5) for all k=0,...,n-1. (Such a sequence is called a very(5,r) sequence. See the link.).

1, 3, 6, 10, 13, 16

Offset

1,2

Comments

Conjecture. Let A be a very(5,1) (respectively very(5,4)) sequence of length n and let Z be a sequence of n-1 0's.. Then AZ(3A)ZA is a very(5,1) (respectively very(5,4)) sequence of length 5n-2. (Here 3A denotes the result of multiplying each term of A by 3, then reducing modulo 5; and juxtaposition of symbols denotes concatenation of sequences.)

Links

Table of n, a(n) for n=1..6.

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

Crossrefs

Cf. A053006, A117548.

Sequence in context: A310049 A168241 A099822 * A190767 A310050 A356469

Adjacent sequences: A117546 A117547 A117548 * A117550 A117551 A117552

Keyword

nonn,more

Author

John W. Layman, Apr 21 2006

Status

approved