A333211 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, 1, 0, 2, 1, 0, 2, 1, 3, 0, 3, 1, 3, 1, 1, 13, 0, 6, 1, 0, 2, 1, 14, 0, 3, 1, 12, 0, 3, 1, 4, 0, 3, 1, 4, 4, 0, 4, 1, 4, 1, 1, 27, 0, 6, 1, 27, 4, 0, 4, 1, 10, 0, 3, 1, 21, 0, 3, 1, 4, 9, 0, 4, 1, 4, 1, 1, 25, 0, 6, 1, 25, 4, 0, 4, 1, 10, 25

Offset

1,7

Comments

After 100 million terms the smallest number not appearing is 179549, while the smallest product of adjacent terms not appearing is 2969.

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 product of two adjacent terms.
a(4) = 1 as a(2)*a(3) = 0*0 = 0, which equals the product a(1)*a(2), one term back from a(3).
a(5) = 1 as a(3)*a(4) = 0*1 = 0, which equals the product a(2)*a(3), one term back from a(3).
a(6) = 0 as a(4)*a(5) = 1*1 = 1, which has not previously appeared as the product of two adjacent terms.
a(19) = 13 as a(17)*a(18) = 1*1 = 1, which equals the product a(4)*a(5), thirteen terms back from a(18).

Crossrefs

Cf. A181391, A171898, A308721, A333210.

Sequence in context: A215345 A022329 A087466 * A258033 A153248 A221179

Adjacent sequences: A333208 A333209 A333210 * A333212 A333213 A333214

Keyword

nonn

Author

Scott R. Shannon, Mar 11 2020

Status

approved