A359634 - OEIS

%I #25 Mar 09 2023 04:21:11

%S 1,1,2,2,3,3,4,3,4,5,4,5,6,4,5,6,7,6,7,8,5,7,8,9,7,6,8,9,10,6,9,10,11,

%T 9,8,10,11,12,9,10,9,11,12,13,7,12,13,14,12,11,13,14,15,11,13,11,14,

%U 15,16,13,6,14,13,15,16,17,13,15,12,16,17,18,15,8,16,14,17,18,19,15,16,12,17,14,18,19,20

%N a(0)=1 and thereafter a(n) is the length of the longest contiguous group of terms in the sequence thus far that add up to n; if no such group exists, set a(n)=0.

%C If a zero appears, it is not counted as a term in a contiguous grouping. For example, if (10, 30, 0, 60) is our longest group to sum to 100, this counts as 3 terms, not 4. However, in 50 million terms (computed by _Kevin Ryde_), a zero has not appeared. Why is this?

%C How does the lower envelope of this sequence behave?

%H Rémy Sigrist, <a href="/A359634/b359634.txt">Table of n, a(n) for n = 0..10000</a>

%H Rémy Sigrist, <a href="/A359634/a359634.txt">C program</a>

%e a(6) is 4 because in the sequence thus far (1,1,2,2,3,3), the longest run of consecutive terms that sums to 6 is (1,1,2,2), which is 4 terms.

%o (C) See Links section.

%Y Cf. A331614, A358537. a(1-16) in A138099 are the same.

%K nonn

%O 0,3

%A _Neal Gersh Tolunsky_, Jan 08 2023