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A023108 Positive integers which apparently never result in a palindrome under repeated applications of the function f(x) = x + (x with digits reversed). 62
196, 295, 394, 493, 592, 689, 691, 788, 790, 879, 887, 978, 986, 1495, 1497, 1585, 1587, 1675, 1677, 1765, 1767, 1855, 1857, 1945, 1947, 1997, 2494, 2496, 2584, 2586, 2674, 2676, 2764, 2766, 2854, 2856, 2944, 2946, 2996, 3493, 3495, 3583, 3585, 3673, 3675 (list; graph; refs; listen; history; text; internal format)



Also called Lychrel numbers, though the definition of "Lychrel number" varies: Purists only call the "seeds" or "root numbers" Lychrel; the "related" or "extra" numbers (arising in the former's orbit) have been coined "Kin numbers" by Koji Yamashita. There are only 2 "root" Lychrels below 1000 and 3 more below 10000, cf. A088753. - M. F. Hasler, Dec 04 2007

Question: when do numbers in this sequence start to outnumber numbers that are not in the sequence? - J. Lowell, May 15 2014

Answer: according to Doucette's site, 10-digit numbers have 49.61% of Lychrels. So beyond 10 digits, Lychrels start to outnumber non-Lychrels. Dmitry Kamenetsky, Oct 12 2015


F. Gruenberger, Computer Recreations, Scientific American, 250 (No. 4, 1984), 19-26.

R. K. Guy, What's left?, preprint, 1998.

Daniel Lignon, Dictionnaire de (presque) tous les nombres entiers, Ellipses, Paris, 2012, 702 pages. See Entry 196.


Table of n, a(n) for n=1..45.

Jason Doucette, World Records

Martianus Frederic Ezerman, Bertrand Meyer and Patrick Sole, On Polynomial Pairs of Integers, arXiv http://arxiv.org/abs/1210.7593 [math.NT]. 2012.

P. De Geest, Some thematic websources

James Grime and Brady Haran, What's special about 196?, Numberphile video (2015).

T. Irvin, About Two Months of Computing, or An Addendum to Mr. Walker's Three Years of Computing

Wade VanLandingham, 196 and other Lychrel numbers

Project Euler, Problem 55: How many Lychrel numbers are there below ten-thousand?

Wade VanLandingham, Largest known Lychrel number

J. Walker, Three Years Of Computing: Final Report On The Palindrome Quest

Eric Weisstein's World of Mathematics, 196 Algorithm.

Eric Weisstein's World of Mathematics, Palindromic Number Conjecture

Eric Weisstein's World of Mathematics, Lychrel Number

Index entries for sequences related to Reverse and Add!


Cf. A006960, A088753, A063048, A089694, A089521, A023109. A075421, A030547.

Sequence in context: A224667 A118781 A119667 * A092231 A188247 A211851

Adjacent sequences:  A023105 A023106 A023107 * A023109 A023110 A023111




David W. Wilson


196 is conjectured to be smallest initial term which does not lead to a palindrome. John Walker, Tim Irvin and others have extended this to millions of digits without finding one (see A006960).

Edited by M. F. Hasler, Dec 04 2007



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Last modified February 27 06:25 EST 2017. Contains 282704 sequences.