A082215 Concatenation of terms of A018238.

1, 121, 1213121, 121312141213121, 1213121412131215121312141213121, 121312141213121512131214121312161213121412131215121312141213121, 1213121412131215121312141213121612131214121312151213121412131217121312141213121512131214121312161213121412131215121312141213121

Offset: 1

Author

Amarnath Murthy, Apr 08 2003

Keywords

• base
• nonn

Comments

Also called Zimin words.

a(n) is a palindrome for n<10; it is debatable whether a(n) can be called a Zimin word for n>=10 (see the Comments in A018238). - Danny Rorabaugh, Sep 26 2015

Links

• J. Cooper and D. Rorabaugh, Bounds on Zimin Word Avoidance, arXiv:1409.3080 [math.CO], 2014; Congressus Numerantium, 222 (2014), 87-95.
• L. J. Cummings and M. Mays, A one-sided Zimin construction, Electron. J. Combin. 8 (2001), #R27.
• A. I. Zimin, Blocking sets of terms, Math. USSR Sbornik, 47 (1984), No. 2, 353-364.

Crossrefs

Cf. A018238, A123121, A033564.

See A001511 for another representation of this sequence of digits.

Programs

Mathematica

a = {1}; Do[w = IntegerDigits@ a[[n - 1]]; AppendTo[a, FromDigits@ Join[w, IntegerDigits@ n, w]], {n, 2, 7}]; a (* Michael De Vlieger, Sep 26 2015 *)

Formula

The Zimin words are defined here by Z_1 = 1, Z_n = Z_{n-1}nZ_{n-1}. - Dmitry Kamenetsky, Sep 30 2006

Extensions

More terms from Joshua Zucker, May 08 2006

"Palindromes" replaced with "Numbers" in sequence name by Danny Rorabaugh, Sep 26 2015

Shorter name by Joerg Arndt, Aug 28 2021