A357064 - OEIS

%I #23 Oct 25 2022 05:13:25

%S 1,2,3,7,418090195952691922788354

%N a(n) = k such that A091411(k) = A091409(n).

%C The existence of a(n) is proven in Lemma 1.2(a) of the article "The first occurrence of a number in Gijswijt's sequence". There, it is called t^{(1)}(n). In this article, a formula for the numbers t^{(m)}(n) is given. It looks like a tower of exponents and can be found in Theorem 6.20. This formula is then used to find a formula for the first occurrence of an integer n in Gijswijt's sequence, which is A091409(n).

%C The value of a(5) is calculated in Subsection 8.2 of the same article.

%C The value of a(6) is larger than 10^(10^100), so it would be impossible to include here.

%H Levi van de Pol, <a href="https://arxiv.org/abs/2209.04657">The first occurrence of a number in Gijswijt's sequence</a>, arXiv:2209.04657 [math.CO], 2022.

%e For n=4 we have A091411(7)=A091409(4). Therefore, a(4)=7.

%Y Cf. A091409, A091411.

%K nonn

%O 1,2

%A _Levi van de Pol_, Sep 10 2022