New Jersey United States Member #71646 March 1, 2009 204 Posts Offline

Posted: January 6, 2010, 5:05 pm - IP Logged

"68 is a member of an iteratively-defined sequence called the Perrin(or Ondrej Such) numbers. It is defined in a similar way to theFibonacci and Pell numbers: A_{0} = 0; A_{1}= 2; A_{2} = 3; A_{N+1} = A_{N-1} + A_{N-2}. Thesequence starts: 3, 0, 2, 3, 2, 5, 5, 7,10, 12, 17, 22, 29,39, 51, 68, 90, 119, 158,209, 277, 367, ... (Sloane's A001608; myMCS197664). Because it has the same iteration rule asthe Padovan numbers, both have the same asymtotic ratio,about 1.3247."

In trying to learn about the properties of the number 68, I came across the above statement. Problem is I don't know what it means. Can anyone break this down for me?

"Bless me Lord, so that I may be a blessing to others."

United States Member #47420 November 4, 2006 3930 Posts Offline

Posted: January 6, 2010, 5:12 pm - IP Logged

Do you really care what this means?..I must be the dumbest boob around cause I have no idea what it means..You would need a dictionary to figure out what some of the wortds mean..Good luck and hope you figure it out but don't know why?..Hope you bust a big one someday..

United States Member #58857 February 27, 2008 112 Posts Offline

Posted: January 6, 2010, 6:07 pm - IP Logged

When it doubt, ask Wikipedia.

Sixty-eight is a nontotient. It is also a Perrin number, preceded in the sequence by 29, 39, 51 (it is the sum of the first two mentioned). It is also a Happy number.

All of the numbers except for the first three have an important pattern.

3+2=5, 2+3=5, 2+5=7, 5+5=10, 5+7=12, 7+10=22...29+39=68 etc, etc.

So if you take a number in the pattern and go back 3 numbers the third previous number and the second previous number will add up to it example 29+39=68, if you picked 119 skip 90 and 51+68=119. I hope that explains it, sorry if it doesn't I'm bad at explaining things. As to why Perrin numbers are important, I believe they helped mathematicians to find prime numbers.

New Jersey United States Member #71646 March 1, 2009 204 Posts Offline

Posted: January 6, 2010, 7:24 pm - IP Logged

Quote: Originally posted by tiggs95 on January 6, 2010

Do you really care what this means?..I must be the dumbest boob around cause I have no idea what it means..You would need a dictionary to figure out what some of the wortds mean..Good luck and hope you figure it out but don't know why?..Hope you bust a big one someday..

Yes I do care because I had a dream (posted in Mystical) which seems to stump everyone cause no one can tell me what it means or even offer an opinion of what it means. The number 68 was in my dream and I can't figure out why so I was trying to do my own research on it.

"Bless me Lord, so that I may be a blessing to others."

New Jersey United States Member #71646 March 1, 2009 204 Posts Offline

Posted: January 6, 2010, 7:39 pm - IP Logged

Quote: Originally posted by Pinkpansies on January 6, 2010

When it doubt, ask Wikipedia.

Sixty-eight is a nontotient. It is also a Perrin number, preceded in the sequence by 29, 39, 51 (it is the sum of the first two mentioned). It is also a Happy number.

All of the numbers except for the first three have an important pattern.

3+2=5, 2+3=5, 2+5=7, 5+5=10, 5+7=12, 7+10=22...29+39=68 etc, etc.

So if you take a number in the pattern and go back 3 numbers the third previous number and the second previous number will add up to it example 29+39=68, if you picked 119 skip 90 and 51+68=119. I hope that explains it, sorry if it doesn't I'm bad at explaining things. As to why Perrin numbers are important, I believe they helped mathematicians to find prime numbers.

Thank you so much for this I am going to study it further.

"Bless me Lord, so that I may be a blessing to others."

United States Member #83701 December 13, 2009 225 Posts Offline

Posted: January 6, 2010, 9:13 pm - IP Logged

Quote: Originally posted by Pinkpansies on January 6, 2010

When it doubt, ask Wikipedia.

Sixty-eight is a nontotient. It is also a Perrin number, preceded in the sequence by 29, 39, 51 (it is the sum of the first two mentioned). It is also a Happy number.

All of the numbers except for the first three have an important pattern.

3+2=5, 2+3=5, 2+5=7, 5+5=10, 5+7=12, 7+10=22...29+39=68 etc, etc.

So if you take a number in the pattern and go back 3 numbers the third previous number and the second previous number will add up to it example 29+39=68, if you picked 119 skip 90 and 51+68=119. I hope that explains it, sorry if it doesn't I'm bad at explaining things. As to why Perrin numbers are important, I believe they helped mathematicians to find prime numbers.

I must be missing something here, when X=1, the result of (3-X^{2})/(1-X^{2}-X^{3}) is -2. This is because the square and cube of 1 is still 1 so the numerator works out to be 2 and the denominator works out to be -1. So starting with 0, I get the sequence of:

3, -2, 1/11, 6/35, 13/79, 22/149 ...

The number 68 does bring up the joke that 68 is the speed limit of love making because it flips around at 69.

I think the closest they got to an equation that gives you prime numbers was Carmichaels primes or Fermats pseudoprimes. Basically using modulus to attempt to estimate if it's a prime number or not. The problem is that there are false positives in this test which still must be ruled out by a traditional sieve approach. Still it's a hell of a lot better than the usual approach of trying to reduce the search space, ie.: testing versus previously found primes but searching only up to the square root of the number being tested etc. It did occur to me once that you should be able to estimate the interval to the next prime number based on the greatest known prime and all the prime numbers less than a certain proportion of that prime perhaps a square root, but I never actually sat down and worked that out.

Pity we don't have Fermat working on predicting lottery numbers.

United States Member #58857 February 27, 2008 112 Posts Offline

Posted: January 7, 2010, 8:14 am - IP Logged

Quote: Originally posted by jwhou on January 6, 2010

I must be missing something here, when X=1, the result of (3-X^{2})/(1-X^{2}-X^{3}) is -2. This is because the square and cube of 1 is still 1 so the numerator works out to be 2 and the denominator works out to be -1. So starting with 0, I get the sequence of:

3, -2, 1/11, 6/35, 13/79, 22/149 ...

The number 68 does bring up the joke that 68 is the speed limit of love making because it flips around at 69.

I think the closest they got to an equation that gives you prime numbers was Carmichaels primes or Fermats pseudoprimes. Basically using modulus to attempt to estimate if it's a prime number or not. The problem is that there are false positives in this test which still must be ruled out by a traditional sieve approach. Still it's a hell of a lot better than the usual approach of trying to reduce the search space, ie.: testing versus previously found primes but searching only up to the square root of the number being tested etc. It did occur to me once that you should be able to estimate the interval to the next prime number based on the greatest known prime and all the prime numbers less than a certain proportion of that prime perhaps a square root, but I never actually sat down and worked that out.

Pity we don't have Fermat working on predicting lottery numbers.

Sorry, you're right. I was not able to transfer the full sequence. If you are interested in it go to Wikipedia and look up "Perrin numbers". The version I posted was the overall simplified form. It is a complex equation. I actually just plugged in the 0 and made sure it checked out.

Use Mirror #'s Use prs. with your Key* numbers the most Vivid thing in your dream go up or down on #'s. Flip 6=9 `9=6 Bullseyes 0 or 1 for Pick 4 and the P. 5 Play the other part of doubles. Do the Whole nine yards for a P. 4* P. 5* or 0 thur 9 for P. 4 P. 5 from my dreams or hunches good Luck.. Write your Dreams down Play for 3 days. Good Luck All.

Use Mirror #'s Use prs. with your Key* numbers the most Vivid thing in your dream go up or down on #'s. Flip 6=9 `9=6 Bullseyes 0 or 1 for Pick 4 and the P. 5 Play the other part of doubles. Do the Whole nine yards for a P. 4* P. 5* or 0 thur 9 for P. 4 P. 5 from my dreams or hunches good Luck.. Write your Dreams down Play for 3 days. Good Luck All.

Use Mirror #'s Use prs. with your Key* numbers the most Vivid thing in your dream go up or down on #'s. Flip 6=9 `9=6 Bullseyes 0 or 1 for Pick 4 and the P. 5 Play the other part of doubles. Do the Whole nine yards for a P. 4* P. 5* or 0 thur 9 for P. 4 P. 5 from my dreams or hunches good Luck.. Write your Dreams down Play for 3 days. Good Luck All.

Use Mirror #'s Use prs. with your Key* numbers the most Vivid thing in your dream go up or down on #'s. Flip 6=9 `9=6 Bullseyes 0 or 1 for Pick 4 and the P. 5 Play the other part of doubles. Do the Whole nine yards for a P. 4* P. 5* or 0 thur 9 for P. 4 P. 5 from my dreams or hunches good Luck.. Write your Dreams down Play for 3 days. Good Luck All.