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A065001 a(n) = (presumed) number of palindromes in the 'Reverse and Add!' trajectory of n, or -1 if this number is not finite.

%I A065001 #8 May 10 2025 23:14:15
%S A065001 11,10,8,9,10,7,6,8,4,9,9,6,7,5,5,7,6,3,4,8,6,8,5,5,7,6,3,4,4,6,7,5,6,
%T A065001 7,6,3,4,4,4,7,5,5,7,7,3,4,4,4,2,5,5,7,6,3,5,4,4,2,6,5,7,6,3,4,4,5,2,
%U A065001 6,3,7,6,3,4,4,4,2,7,3,5,6,3,4,4,4,2,6,3,6,1,3,4,4,4,2,6,3,5,1,3,8,8,6,6
%N A065001 a(n) = (presumed) number of palindromes in the 'Reverse and Add!' trajectory of n, or -1 if this number is not finite.
%C A065001 Presumably a(196) = 0 (see A016016). Conjecture: There is no n > 0 such that the trajectory of n contains an infinite number of palindromes; the trajectory of n eventually leads to a term in the trajectory of some integer k which belongs to sequence A063048, i.e. whose trajectory (presumably) never leads to a palindrome.
%H A065001 <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%e A065001 8, 77, 1111, 2222, 4444, 8888, 661166, 3654563 are the eight palindromes in the trajectory of 8 and 3654563 + 3654563 = 7309126 is the sixth term in the trajectory of 10577 (see A063433) which (presumably) never leads to a palindrome (see A063048), so a(8) = 8.
%o A065001 (ARIBAS) maxarg := 120; stop := 500; for k := 1 to maxarg do n := k; count := 0; c := 0; while c < stop do if n = int_reverse(n) then inc(count); c := 0; end; inc(c); n := n + int_reverse(n); end; write(count," " ); end;
%Y A065001 A002113, A016016, A033865, A023108, A063048, A063433.
%K A065001 base,nonn
%O A065001 1,1
%A A065001 _Klaus Brockhaus_, Nov 01 2001