A333359 Variation of Van Eck's sequence A181391: a(n+1) = the minimum positive offset m from a(n) such that the decimal concatenation of a(n-m), a(n-m+1), ..., a(n-m+k) = a(n), where k >= 0; a(n+1)=0 if no such m exists. Start with a(1)=0.

0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6, 5, 4, 0, 5, 3, 0, 3, 2, 9, 0, 4, 9, 3, 6, 14, 0, 6, 3, 5, 15, 0, 5, 3, 5, 2, 17, 0, 6, 11, 0, 3, 8, 0, 3, 3, 1, 42, 0, 5, 15, 20, 51, 0, 5, 5, 1, 10, 59, 0, 6, 22, 59, 4, 42, 17, 29, 48, 0, 9, 47, 0, 3, 27, 0, 3, 3, 1, 21, 75, 0, 6

Offset: 1

Author

Scott R. Shannon, Mar 16 2020

Keywords

• nonn
• base

Comments

The terms up to a(56) are the same as A181391 but vary from a(57) and beyond. After 10000 terms the smallest number not appearing is 332.

Examples

			a(42) = 0 as a(41) = 17, and neither '17' or adjacent sequence terms '1' and '7' appear earlier in the sequence.
a(57) = 51 as a(56) = 20, and the value '20' is the concatenation of a(5) = 2 and a(6) = 0, and a(5) is fifty-one terms back from a(56).
		

Links

• Brady Haran and N. J. A. Sloane, Don't Know (the Van Eck Sequence), Numberphile video (2019).

Crossrefs

Cf. A181391, A007908, A001704.