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2017-05-16, 16:52   #1
MattcAnderson

"Matthew Anderson"
Dec 2010
Oregon, USA

71410 Posts
This is a sequence with integers

Hi Mersenneforum,

Maple software is so overwhelming. It can algebraically solve almost anything. I don't type Pari much. But I try to shine a light on some math / computer topics.

Regards,
Matt
Attached Files
 fibonacci with coefficients again 4.pdf (123.6 KB, 156 views)

2017-05-17, 00:00   #2
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

838410 Posts

Quote:
 Originally Posted by MattcAnderson Hi Mersenneforum, Maple software is so overwhelming. It can algebraically solve almost anything. I don't type Pari much. But I try to shine a light on some math / computer topics. Request for comments. Regards, Matt
you can reduce both the start values by a factor of two as well as the recurrence relationship and get the odd part of the values given.

x1=1
x2=3
x[a]=6*x[a-1]+5*x[a-2]

x[3]=18+5 =23
x[4]=138+15 =153

etc. edit:okay maybe not but you do eliminate a constant factor of two and get another recurrence that is always odd.

Last fiddled with by science_man_88 on 2017-05-17 at 00:02

 2017-05-17, 13:11 #3 science_man_88     "Forget I exist" Jul 2009 Dumbassville 26×131 Posts more generally there are 4 ways for the first values to be setup within the integers mod 2 1 0 1 1 0 0 0 1 and 4 ways for the coefficients ( same as above) these combinations result in: Code: (10:02) gp > my(a=[0,0]);for(x=1,10,a=concat(a,1*a[#a]+0*a[#a-1]));a %1 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] (10:03) gp > my(a=[0,1]);for(x=1,10,a=concat(a,1*a[#a]+0*a[#a-1]));a %2 = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (10:03) gp > my(a=[1,1]);for(x=1,10,a=concat(a,1*a[#a]+0*a[#a-1]));a %3 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (10:03) gp > my(a=[1,0]);for(x=1,10,a=concat(a,1*a[#a]+0*a[#a-1]));a %4 = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] (10:03) gp > my(a=[1,0]);for(x=1,10,a=concat(a,0*a[#a]+0*a[#a-1]));a %5 = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] (10:04) gp > my(a=[1,1]);for(x=1,10,a=concat(a,0*a[#a]+0*a[#a-1]));a %6 = [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] (10:04) gp > my(a=[0,1]);for(x=1,10,a=concat(a,0*a[#a]+0*a[#a-1]));a %7 = [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] (10:04) gp > my(a=[0,0]);for(x=1,10,a=concat(a,0*a[#a]+0*a[#a-1]));a %8 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] (10:04) gp > my(a=[0,0]);for(x=1,10,a=concat(a,0*a[#a]+1*a[#a-1]));a %9 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] (10:05) gp > my(a=[1,0]);for(x=1,10,a=concat(a,0*a[#a]+1*a[#a-1]));a %10 = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0] (10:05) gp > my(a=[0,1]);for(x=1,10,a=concat(a,0*a[#a]+1*a[#a-1]));a %11 = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1] (10:05) gp > my(a=[1,1]);for(x=1,10,a=concat(a,0*a[#a]+1*a[#a-1]));a %12 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (10:05) gp > my(a=[1,1]);for(x=1,10,a=concat(a,1*a[#a]+1*a[#a-1]));a %13 = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144] (10:06) gp > my(a=[0,1]);for(x=1,10,a=concat(a,1*a[#a]+1*a[#a-1]));a %14 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89] (10:06) gp > my(a=[0,0]);for(x=1,10,a=concat(a,1*a[#a]+1*a[#a-1]));a %15 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] (10:06) gp > my(a=[1,0]);for(x=1,10,a=concat(a,1*a[#a]+1*a[#a-1]));a %16 = [1, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55] with the ones that don't result in 0 and 1 equating to 1,1,0,1,1,0,1,1,0,1,1,0 and 0,1,1,0,1,1,0,1,1,0,1,1 and 1,0,1,1,0,1,1,0,1,1,0 when done mod 2.
 2017-05-17, 13:31 #4 Harrywill   "Harry Willam" May 2017 USA 22·5 Posts Draw one line on this equation to make it correct 5+5+5+5= 555 Last fiddled with by Harrywill on 2017-05-17 at 13:35
2017-05-17, 14:09   #5
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by Harrywill Draw one line on this equation to make it correct $5+5+5+5\neq 555$
now how does it relate to the topic ?

2017-05-17, 15:49   #6
LaurV
Romulan Interpreter

Jun 2011
Thailand

33×347 Posts

Quote:
 Originally Posted by Harrywill Draw one line on this equation to make it correct 5+5+5+5= 555
repeat after me: B, A, N

2017-05-18, 08:33   #7
kar_bon

Mar 2006
Germany

1011010000012 Posts

Quote:
 Originally Posted by science_man_88 now how does it relate to the topic ?
[offtopc]Connect the upper and left line end points of one plus sign.[/offtopc]

Last fiddled with by kar_bon on 2017-05-18 at 08:34

2017-05-23, 21:38   #8
MattcAnderson

"Matthew Anderson"
Dec 2010
Oregon, USA

2·3·7·17 Posts

Hi Mersenneforum,

So here is another Fibonacci like sequence with different starting values.

Regards,
Matt
Attached Files
 Fibonacci like sequence starting with 2 and 2.pdf (83.6 KB, 179 views)

2017-05-23, 21:59   #9
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by MattcAnderson Hi Mersenneforum, So here is another Fibonacci like sequence with different starting values. Regards, Matt
you'll note not that other than 2 no other entries in this sequence are prime. They are in fact twice the normal Fibonacci numbers.

2017-05-27, 01:39   #10
MattcAnderson

"Matthew Anderson"
Dec 2010
Oregon, USA

2·3·7·17 Posts

Hi Mersenneforum and others,

New sequence, new integers

This one is c(r) = 8*c(r-1)+9*c(r-2).

I am not saying that there is any special significance in this one, but check it out.

Regards,

Matt
Attached Files
 Fibonacci with 8 and 9.pdf (67.9 KB, 143 views)

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