VOOZH about

URL: https://oeis.org/A333210

⇱ A333210 - OEIS

login
A333210
Variation of Van Eck's sequence A181391: a(n+1) = the minimum positive offset m from a(n) such that a(n-m-1)+a(n-m) = a(n-1)+a(n); a(n+1)=0 if no such m exists. Start with a(1) = a(2) = 0.
3
0, 0, 0, 1, 0, 1, 1, 0, 2, 2, 0, 2, 1, 0, 6, 0, 1, 3, 8, 0, 0, 18, 0, 1, 7, 5, 0, 0, 7, 0, 1, 7, 7, 0, 4, 17, 0, 0, 10, 0, 1, 10, 23, 0, 0, 7, 12, 0, 22, 0, 1, 10, 10, 0, 14, 22, 0, 7, 12, 12, 0, 13, 0, 1, 13, 10, 22, 0, 11, 17, 0, 34, 0, 1, 10, 6, 0, 61, 0, 1, 6, 23, 0, 17, 13, 0, 23, 4, 0, 54, 0, 1, 12
OFFSET
1,9
COMMENTS
After 100 million terms the smallest number not appearing is 381884, while the smallest sum of adjacent terms not appearing is 487833.
LINKS
Brady Haran and N. J. A. Sloane, Don't Know (the Van Eck Sequence), Numberphile video (2019).
EXAMPLE
a(3) = 0 as a(1)+a(2) = 0+0 = 0, which has not previously appeared as the sum of two adjacent terms.
a(4) = 1 as a(2)+a(3) = 0+0 = 0, which equals the sum a(1)+a(2), one term back from a(3).
a(5) = 0 as a(3)+a(4) = 0+1 = 1, which has not previously appeared as the sum of two adjacent terms.
a(6) = 1 as a(4)+a(5) = 1+0 = 1, which equals the sum a(3)+a(4), one term back from a(5).
a(19) = 8 as a(17)+a(18) = 1+3 = 4, which equals the sum a(9)+a(10), eight terms back from a(18).
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Mar 11 2020
STATUS
approved