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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A281978 Lexicographically earliest sequence of distinct terms such that, for any n>0, a(2n) is divisible by a(2n-1) and by a(2n+1). 8
1, 4, 2, 6, 3, 15, 5, 20, 10, 40, 8, 24, 12, 36, 9, 54, 18, 90, 30, 120, 60, 180, 45, 135, 27, 162, 81, 324, 108, 216, 72, 144, 16, 64, 32, 96, 48, 240, 80, 320, 160, 640, 128, 384, 192, 576, 288, 864, 432, 1296, 648, 1944, 243, 972, 486, 1458, 729, 3645, 405 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

To compute a(2n) and a(2n+1): we take the least unseen multiple of a(2n-1) with an unseen proper divisor: the multiple gives a(2n) and the least proger divisor gives a(2n+1).

The first multiple of 2 occurs at n=2: a(2)=4, and a(3)=2.

The first multiple of 3 occurs at n=4: a(4)=6, and a(5)=3,

The first multiple of 5 occurs at n=6: a(6)=15, and a(7)=5.

The first multiple of 7 occurs at n=454: a(454)=5511240, and a(455)=7.

The first multiple of 11 occurs at n=889838: a(889838)=627667978163491186346557440000000000000, and a(889839)=11.

For n>1, let b(n)=least k>0 such that a(n+k)<>a(n)*a(k+1); the first records for b are:

n       b(n)     a(n)

------  -------  ----

2             1  2^2

7             3  5

19            4  2*3*5

33           14  2^4

73           27  5^2

455         243  7

1439        248  7^2

3069        275  7^3

10567       276  7^5

41709       768  7^8

85179      1169  7^10

889839  >110162  11

Conjectures:

- All prime numbers appear in this sequence, in increasing order,

- The derived sequence b is unbounded,

- This sequence is a permutation of the natural numbers.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..25000

Rémy Sigrist, PARI program for A281978

Rémy Sigrist, Logarithmic scatterplot of the first million terms

EXAMPLE

The first terms, alongside their p-adic valuations with respect to p=2, 3, 5 and 7 (with 0's omitted), are:

n       a(n)  v2  v3  v5  v7

---  -------  --  --  --  --

1          1

2          4   2

3          2   1

4          6   1   1

5          3       1

6         15       1   1

7          5           1

8         20   2       1

9         10   1       1

10        40   3       1

11         8   3

12        24   3   1

13        12   2   1

14        36   2   2

15         9       2

16        54   1   3

17        18   1   2

18        90   1   2   1

19        30   1   1   1

20       120   3   1   1

21        60   2   1   1

22       180   2   2   1

23        45       2   1

24       135       3   1

...

451   524880   4   8   1

452  1574640   4   9   1

453   787320   3   9   1

454  5511240   3   9   1   1

455        7               1

456       28   2           1

457       14   1           1

458       42   1   1       1

CROSSREFS

Cf. A036552 (a(2n) is divisible by a(2n-1)).

Sequence in context: A097467 A169839 A275845 * A209877 A273667 A187109

Adjacent sequences:  A281975 A281976 A281977 * A281979 A281980 A281981

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Feb 04 2017

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 February 15 20:32 EST 2019. Contains 320138 sequences. (Running on oeis4.)