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A033865 Start with n; if palindrome, stop; otherwise add to itself with digits reversed; a(n) gives palindrome at which it stops, or -1 if no palindrome is ever reached.

%I A033865 #32 Apr 19 2025 14:38:58
%S A033865 0,1,2,3,4,5,6,7,8,9,11,11,33,44,55,66,77,88,99,121,22,33,22,55,66,77,
%T A033865 88,99,121,121,33,44,55,33,77,88,99,121,121,363,44,55,66,77,44,99,121,
%U A033865 121,363,484,55,66,77,88,99,55,121,363,484,1111,66,77,88,99,121,121,66,484,1111,4884,77,88,99,121,121,363,484,77,4884,44044,88
%N A033865 Start with n; if palindrome, stop; otherwise add to itself with digits reversed; a(n) gives palindrome at which it stops, or -1 if no palindrome is ever reached.
%C A033865 It is believed that a(196) = -1.
%D A033865 M. Donner, I Love Me, Vol. I: S. Wordrow's palindromic encyclopedia (Algonquin Books, 1996) p. 268
%H A033865 T. D. Noe, <a href="/A033865/b033865.txt">Table of n, a(n) for n = 0..195</a>
%H A033865 O. Forster, <a href="http://www.mathematik.uni-muenchen.de/~forster/sw/aribas.html">ARIBAS</a>
%H A033865 Mathforum, <a href="http://mathforum.org/library/drmath/view/51508.html">Making Numbers into Palindromic Numbers</a>
%H A033865 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/196-Algorithm.html">196-Algorithm.</a>
%e A033865 19 -> 19 + 91 = 110 -> 110 + 011 = 121, so a(19) = 121.
%t A033865 Table[NestWhile[# + FromDigits[Reverse[IntegerDigits[#]]] &, n, IntegerDigits[#] != Reverse[IntegerDigits[#]] &], {n, 0, 90}] (* _Harvey P. Dale_, Dec 18 2011 *)
%o A033865 (ARIBAS) var st: stack; end; for k := 0 to 60 do n := k; while n <> int_reverse(n) do n := n + int_reverse(n); end; stack_push(st,n); end; stack2array(st);
%o A033865 (PARI) a(n)=my(k); while((k=fromdigits(Vecrev(digits(n)))) != n, n += k); n \\ infinite loop if a(n) = -1; _Charles R Greathouse IV_, Dec 13 2015
%Y A033865 Cf. A061563, A016016, A023109, A006960, A023108, A002113, A033665 (number of steps).
%K A033865 nonn,base,nice
%O A033865 0,3
%A A033865 _David W. Wilson_
%E A033865 More terms from Jenise Smalley (neicey01(AT)hotmail.com), Oct 18 2001