UlamSequence | Example Notebook

Basic Examples
(2)

Let

u=1

and

v=1

. Call the sequence

s

n

. Then

s

1

=1

and

s

2

=2

:

In[14]:=

[◼]	UlamSequence

[2,{1,2}]

Out[14]=

{1,2}

For term 3, there is only one sum,

3=1+2

, so

s

3

=3

:

In[15]:=

[◼]	UlamSequence

[3,{1,2}]

Out[15]=

{1,2,3}

For term 4, only the sum

1+3

gives

4

, so

s

4

=4

. The sum

2+2

is not a sum of unique previous terms:

In[16]:=

[◼]	UlamSequence

[4,{1,2}]

Out[16]=

{1,2,3,4}

For term 5, the two sums

1+4

and

2+3

give

5

, so

s

5

≠5

. The sum

2+4

is

6

; the sum

1+2+3=6

has more than one summand, so

s

5

=6

:

In[17]:=

[◼]	UlamSequence

[6,{1,2}]

Out[17]=

{1,2,3,4,6}

———

Here are the terms up to 1000:

In[18]:=

[◼]	UlamSequence

[1000,{1,2}]

Out[18]=

{1,2,3,4,6,8,11,13,16,18,26,28,36,38,47,48,53,57,62,69,72,77,82,87,97,99,102,106,114,126,131,138,145,148,155,175,177,180,182,189,197,206,209,219,221,236,238,241,243,253,258,260,273,282,309,316,319,324,339,341,356,358,363,370,382,390,400,402,409,412,414,429,431,434,441,451,456,483,485,497,502,522,524,544,546,566,568,585,602,605,607,612,624,627,646,668,673,685,688,690,695,720,722,732,734,739,751,781,783,798,800,820,847,849,861,864,866,891,893,905,927,949,983,986,991}

The plot is wrinkly:

In[64]:=

ListLinePlot[%]

Out[64]=

Basic Examples (2)

Scope (2) 

Basic Examples
(2)

Scope
(2)

