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A225538 Let r(n) denote the reverse of n. For every n, consider the sequence n_1 = n + 1 + r(n+1), and for m >= 2, n_m = n_(m-1) + 1 + r(n_(m-1) + 1). a(n) is the least m for which n_m is a palindrome, or 0 if there is no such m. 1

%I #22 Sep 03 2018 23:00:02

%S 1,1,1,1,2,2,2,2,3,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,

%T 1,1,2,1,2,1,1,1,1,1,1,2,1,2,2,1,1,1,1,1,2,1,2,2,4,1,1,1,1,2,1,2,2,4,

%U 7,1,1,1,2,1,2,2,4,7,10,1,1,2,1,2,2,4,7

%N Let r(n) denote the reverse of n. For every n, consider the sequence n_1 = n + 1 + r(n+1), and for m >= 2, n_m = n_(m-1) + 1 + r(n_(m-1) + 1). a(n) is the least m for which n_m is a palindrome, or 0 if there is no such m.

%C Conjecture: the least n's for which a(n) = 0 are 1895, 1985, 2894, 2984, 3893, and 3983. - _Peter J. C. Moses_, May 10 2013

%C See analogous numbers in A023108 for which the so-called Lychrel process "Reverse and Add!", apparently, never leads to a palindrome.

%H Peter J. C. Moses, <a href="/A225538/b225538.txt">Table of n, a(n) for n = 0..5000</a>

%e For n=8, 9 + 9 = 18, 19 + 91 = 110, 111 + 111 = 222 is a palindrome. Thus a(8)=3.

%Y Cf. A023108.

%K nonn,base

%O 0,5

%A _Vladimir Shevelev_, May 10 2013

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