A357064 a(n) = k such that A091411(k) = A091409(n).

1, 2, 3, 7, 418090195952691922788354

Offset

1,2

Comments

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).

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

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

Links

Table of n, a(n) for n=1..5.

Levi van de Pol, The first occurrence of a number in Gijswijt's sequence, arXiv:2209.04657 [math.CO], 2022.

Levi van de Pol, The Growth Rate of Gijswijt's Sequence, J. Int. Seq. (2025) Vol. 28, Art. No. 25.4.6. See p. 7.

Example

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

Crossrefs

Cf. A091409, A091411.

Sequence in context: A048979 A201363 A088332 * A131959 A202688 A021046

Adjacent sequences: A357061 A357062 A357063 * A357065 A357066 A357067

Keyword

nonn

Author

Levi van de Pol, Sep 10 2022

Status

approved