A357063 -id:A357063 - 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".

A091588 A smoothed version of A091587.

Original entry on oeis.org

1, 3, 8, 24, 67, 195, 580, 1730, 5179, 15533, 46578, 139712, 419115, 1257319, 3771930, 11315764, 33947261, 101841751, 305525228, 916575642, 2749726883

Offset: 0

N. J. A. Sloane, Mar 05 2004

Each term is roughly 3 times the previous term.

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), #07.1.2.
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 [pdf, ps].
Levi van de Pol, The first occurrence of a number in Gijswijt's sequence, arXiv:2209.04657 [math.CO], 2022.
Index entries for sequences related to Gijswijt's sequence

Records in A091839. Cf. A090822, A091587, A091587, A217590.

a(n+1) = a(n) + A357063(n+1) + A091840(n+1). See Conjecture 4.2 of F. J. van de Bult et al., proved p. 54 of Levi van de Pol. - Levi van de Pol, Nov 04 2022

a(10)-a(13) from Allan Wilks, Mar 10 2004
a(14)-a(20) from Alexander Staunton, Apr 09 2022
Removed an incorrect program. - N. J. A. Sloane, Aug 20 2022

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula