A018238 Add 1 to leading digit and put in front.

1, 21, 3121, 41213121, 5121312141213121, 61213121412131215121312141213121, 7121312141213121512131214121312161213121412131215121312141213121

Offset: 1

Author

N. J. A. Sloane, Michael Minic (minic(AT)mtsu.edu)

Keywords

• nonn
• base

Comments

The concatenation of first n terms (if n is small) yields a palindrome: 1, 121, 1213121, etc. - Amarnath Murthy, Apr 08 2003

From M. F. Hasler, May 05 2008: (Start)

This is not the case from n=10 on: According to the formula in A123121 A082215(10) has an even number of digits, the middle digits being "10". (In a strict sense, e.g. Def. 3 of the first reference there, A082215(9) is the last Zimin word on the alphabet {1,...,9}, though.)

While there is less ambiguity about the definition of A018238(10), it is not clear if A018238(11) should start with "11..." or with "10..." (the largest digit of all subsequent terms being "9"). According to the formula in A123121, a(100) has 3 digits more than a(99), so the first choice seems appropriate and has been adopted for the given PARI code.

However, it corresponds to a modified definition, "a(n) = concatenation of n and all preceding terms". a(3) is the only prime term up to a(14) included. The sequence is (1,0,1,0,1,0,...) (mod 3), at least up to a(20). (End)

Links

• M. F. Hasler, Table of n, a(n) for n=1,...,11.

Crossrefs

Cf. A001511, A082215, A123121, A033564.

Programs

PARI

A018238(n,t="")=for(k=2,n,t=Str(t,k-1,t));eval(Str(n,t)) \\ M. F. Hasler, May 05 2008