# 196 AND OTHER LYCHREL NUMBERS

## Welcome to p196.org!

We as a group have added quite a few words and phrases to our discussions, and it is becoming apparent, that we need to create some sort of standardization on how we are using these words and phrases...

With the exception of the Blackboard Archive, I have gone through and made an attempt to modify all of the other pages to match these definitions. I'm SURE I missed some. If you notice something on another page that conflicts with what is here, trust this first, and contact me to make the change. THANKS!!

PALINDROME: A number or word that reads the same whether written forwards or backwards.
Example:

REVERSE AND ADD PROCESS: The mathematical operation of reversing a number's digit order, and adding the result to the original number. The resulting sum may or may not be a palindrome. If the sum is not a palindrome, the process can be repeated as many times as desired to possibly form a palindrome.
Examples:

123 + 321 = 444

1845 + 5481 = 7326
7326 + 6237 = 13563
13563 + 36531 = 50094
50094 + 49005 = 99099

196 + 691 = 887
887 + 788 = 1675
1675 + 5761 = 7436
7436 + 6347 = 13783
...

ITERATION: A single complete step in the reverse and add process. It includes the reversing of the digit order, the addition of all digits, and a check to see if a palindrome has been formed.
Examples:

123 + 321 = 444
This problem is solved in 1 iteration.

1845 + 5481 = 7326
7326 + 6237 = 13563
13563 + 36531 = 50094
50094 + 49005 = 99099
This problem is solved in 4 iterations.

196 + 691 = 887
887 + 788 = 1675
1675 + 5761 = 7436
7436 + 6347 = 13783
...
This problem is unsolved after hundreds of millions of iterations.

DELAY: A delay of n takes n iterations to reach a palindrome. This term is used almost exclusively with starting numbers that form palindromes.

LYCHREL NUMBERS: All numbers that do not form a palindrome through the reverse and add process.

NOTE: A Lychrel number MAY BE a palindrome itself.

Examples:

196 (Seed), 295(Kin), 394(Kin), 879 (Seed), 887(Kin), 1997(Seed), 9,999 (Seed)...

SEED NUMBERS: A subset of Lychrel Numbers, that is the smallest number of each non palindrome producing thread. A Seed number may be a palindrome itself.
Examples:

196, 879, 1997...
9999, 99999, 999999

KIN NUMBERS: A subset of Lychrel Numbers, that include all numbers of a thread, except the Seed, or any number that will converge on a given thread after a single iteration. This term was introduced by Koji Yamashita in 1997.
Examples:

295, 394, 493, 978, 2996...

THREAD: The sequence of numbers that may or may not lead to a palindrome through the reverse and add process. Any given Seed and its associated Kin numbers will converge on the same thread. The thread does not include the original Seed or Kin number, but only the numbers that are common to both, after they converge.
Examples:

1845 (Starting Number) and 2844 (Kin) share the thread 7326, 13563, 50094, 99099.

196 (Seed) and 790 (Kin) share the thread 887, 1675, 7436, 13783, 52514... .

295 (Kin) and 4672 (Kin) share the thread 7436, 13783, 52514...

The term was first used by Jason Doucette in private email to Wade in May of 2002.

CONSEQUENCE: A consequence of a number is another number that joins into the same thread.
Example:

691 is a consequence of 196, since after one iteration it joins the thread.

The term was defined by Jason Doucette

BARONE SEQUENCE: A series of consecutive Lychrel numbers, which are evenly spaced with a separation of n. Named after Felipe Barone, whose efforts produced an app that first showed that these sequences exist.
Example:

1000290692, 1000290693, 1000290694, 1000290695, 1000290696, 1000290697 would be a Barone Sequence of 10 digit Seeds, with a separation of 1.
10019246, 10019446, 10019646, 10019846 would be a Barone Sequence of 8 digit Seeds, with a separation of 200.
10059681 (Seed), 10059682 (Seed), 10059683(Kin) would be a Barone Sequence of 8 digit Seed and Kin numbers with a separation of 1.

LYCHREL PAIRING PER SECOND (LPPS) unit: A measure the software speed when running a "Reverse and Add" operation. The operation measured is the number of digit additions per second. This term was coined by Pierre Laurent as a way to compare different applications when running across a network. It helps to compare stand-alone apps with net apps. The reason being, the stand-alone app could actually be quite a bit more efficient, but the net app can take advantage of multiple CPU's to run at a faster overall speed.
Example:

50000 iterations of a 20M digit number done in 1000 seconds is (50000 * 20000000) / 1000 = 1 billion LPPS.