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.

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

Scott R. Shannon, Table of n, a(n) for n = 1..10000.

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

Cf. A181391, A171898, A308721, A333211.

Sequence in context: A273496 A286576 A322523 * A285193 A354947 A213209

Adjacent sequences: A333207 A333208 A333209 * A333211 A333212 A333213

Keyword

nonn

Author

Scott R. Shannon, Mar 11 2020

Status

approved