A357067 -id:A357067 - cp's OEIS frontend

A357068 Decimal expansion of the limit of A357063(k)/3^(k-1) as k goes to infinity.

1, 5, 7, 7, 2, 2, 7, 9, 2, 3, 9, 9, 4, 5, 0, 0, 6, 9, 4, 1, 0

Offset: 1

Levi van de Pol, Oct 24 2022

In the article "The first occurrence of a number in Gijswijt's sequence", this constant is called epsilon_2. Its existence is proved in Theorem 7.2. The constant occurs in a direct formula (Theorem 7.11) for the first occurrence of an integer n in the level-2 Gijswijt sequence A091787.

			1.57722792399450069410...

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

Cf. A091787, A357063, A091840, A357066, A357067.

Equal to 1 + Sum_{k>=1} A091840(k)/3^k. Proved in Corollary 7.3 of the article "The first occurrence of a number in Gijswijt's sequence".

A357065 Numbers k with the following property: the value A091839(k+1) is not a 1 that is obtained from smoothing A091579.

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 8, 9, 10, 11, 13, 15, 16, 17, 18, 19, 21, 23, 24, 25, 26, 27, 29, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 45, 47, 49, 50, 51, 53, 55, 56, 57, 58, 59, 61, 63, 65, 66, 67, 69, 71, 73, 74, 75, 77, 79, 80, 81, 82, 83, 85, 87, 88, 89, 90, 91, 93, 95, 97, 98, 99, 101, 103

Offset: 1

Levi van de Pol, Sep 10 2022

This sequence is the function iota1 in the article "The first occurrence of a number in Gijswijt's sequence" (page 21). For the connection with smoothing, see Subsection 8.1.

			14 is not a term since A091839(14+1) is a 1 obtained from smoothing: in A091579, the eleventh value is 4, which is replaced by 3,1 to obtain the fourteenth and fifteenth terms of A091839.

F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), Article 07.1.2.
Levi van de Pol, The first occurrence of a number in Gijswijt's sequence, arXiv:2209.04657 [math.CO], 2022.

Cf. A091787, A090822, A357066, A357067.

cp's OEIS Frontend

A357068 Decimal expansion of the limit of A357063(k)/3^(k-1) as k goes to infinity.

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