Basic Examples (2)
Basic Examples
(2)
Let and . Call the sequence . Then =1 and =2 :
u=1
v=1
s
n
s
1
s
2
In[14]:=
Out[14]=
{1,2}
For term 3, there is only one sum, , so =3 :
3=1+2
s
3
In[15]:=
Out[15]=
{1,2,3}
For term 4, only the sum gives , so =4. The sum is not a sum of unique previous terms:
1+3
4
s
4
2+2
In[16]:=
Out[16]=
{1,2,3,4}
For term 5, the two sums and give, so ≠5 . The sum is ; the sum has more than one summand, so =6:
1+4
2+3
5
s
5
2+4
6
1+2+3=6
s
5
In[17]:=
Out[17]=
{1,2,3,4,6}
———
Here are the terms up to 1000:
In[18]:=
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]=
Scope (2)
Scope
(2)