login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A306211 Concatenation of the current sequence with the lengths of the runs in the sequence, with a(1) = 1. 16
1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 3, 1, 4, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 3, 1, 4, 1, 2, 1, 1, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Conjecture: All terms are less than or equal to 5. - Peter Kagey, Jan 29 2019

Conjecture: Every number appears! (Based on the analogy with the somewhat similar sequence A090822, where the first 5 appeared at around 10^(10^23) steps). - N. J. A. Sloane, Jan 29 2019

An alternative definition: Start with 1, extend the sequence by appending its RUNS transform, recompute the RUNS transform, append it, repeat. - N. J. A. Sloane, Jan 29 2019

The first time we see 1, 2, 3, 4, 5 is at n=1, 3, 37, 60, 255. After 65 generations (10228800161220 terms) the largest term is 5. The relative frequencies of 1..5 are roughly 0.71, 6.7e-9, 0.23, 1.6e-8, 0.061. 2s and 4s appear to get rarer as n increases. - Benjamin Chaffin, Feb 07 2019

If we record the successive RUNS transforms and concatenate them, we get 1; 2; 2, 1; 2, 2, 1; 2, 2, 1, 2, 1; ..., which is this sequence without the initial 1. - A. D. Skovgaard, Jan 30 2019 (Rephrased by N. J. A. Sloane, Jan 30 2019)

LINKS

Peter Kagey, Table of n, a(n) for n = 1..10029 (first 20 generations)

N. J. A. Sloane, Table of n, a(n) for n = 1..236878 (first 27 generations)

N. J. A. Sloane, Notes on A306211, Feb 01 2019

EXAMPLE

a(2) = 1, since there is a run of length 1 at a(1).

a(3) = 2, since there is a run of length 2 at a(1..2).

a(4..5) = 2, 1, since the runs are as follows:

1, 1, 2  a(1..3)

\__/  |

2,    1  a(4..5)

a(37) = 3, since a(20..22) = 1, 1, 1.

Steps in construction:

[1]  initial sequence

[1]  its run length

.

[1, 1]  concatenation of above is new sequence

[2]  its run length

.

[1, 1, 2] concatenation of above is new sequence

[2, 1]  its run lengths

.

[1, 1, 2, 2, 1]

[2, 2, 1]

.

[1, 1, 2, 2, 1, 2, 2, 1]

[2, 2, 1, 2, 1]

.

[1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1]

[2, 2, 1, 2, 1, 2, 1, 1, 1]

.

[1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1]

[2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3]

.

[1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3]

Comment from N. J. A. Sloane, Jan 31 2019 (start):

The first 9 generations, in compressed notation (see A323477) are:

1

11

112

11221

11221221

1122122122121

1122122122121221212111

1122122122121221212111221212111211113

1122122122121221212111221212111211113221212111211113211113141

... (end)

MAPLE

P:=proc(q) local a, b, c, k, n; a:=[1, 1];

for n from 1 to q do b:=1; c:=[];

for k from 1 to nops(a)-1 do if a[k+1]=a[k] then b:=b+1;

else c:=[op(c), b]; b:=1; fi; od; a:=[op(a), op(c), b]; od;

a; end: P(10); # Paolo P. Lava, Jan 30 2019. P(g) produces generations 1 through g+2.

CROSSREFS

Cf. A000002, A107946, A306215, A090822.

Positions of 3's, 4's, 5's: A323476, A306222, A306223.

Successive generations: A323477, A323478, A306215, A323475, A306333.

See also A323479, A323480, A323481, A323826 (RUNS transform), A323827, A323829 (where n first appears).

Sequence in context: A269570 A243759 A098398 * A131714 A130196 A230866

Adjacent sequences:  A306208 A306209 A306210 * A306212 A306213 A306214

KEYWORD

nonn,nice

AUTHOR

A. D. Skovgaard, Jan 29 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)