cp's OEIS Frontend

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.).

%I A117549 #12 Aug 16 2020 10:25:09
%S A117549 1,3,6,10,13,16
%N 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.).
%C A117549 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.)
%H A117549 John W. Layman, <a href="http://intranet.math.vt.edu/people/layman/sequences/very_br.htm">On A Generalization of Very Odd Sequences</a>
%Y A117549 Cf. A053006, A117548.
%K A117549 nonn,more
%O A117549 1,2
%A A117549 _John W. Layman_, Apr 21 2006