cp's OEIS Frontend

A092212 a(n) = smallest non-palindromic k such that the base-2 Reverse and Add! trajectory of k is palindrome-free and joins the trajectory of A092210(n).

%I A092212 #14 Nov 07 2019 13:25:56
%S A092212 26,65649,89,4193,3599,775,68076,2173
%N A092212 a(n) = smallest non-palindromic k such that the base-2 Reverse and Add! trajectory of k is palindrome-free and joins the trajectory of A092210(n).
%C A092212 Terms a(9) to a(29) are 205796147 (conjectured), 4402, 16720, 1089448, 442, 537, unknown, 1050177, 1575, 28822, unknown, 40573, 1066, 1587, unknown, unknown, 1081, 1082, 1085, 1115, 4185.
%C A092212 a(n) >= A092210(n); a(n) = A092210(n) iff the trajectory of A092210(n) is palindrome-free, i.e., A092210(n) is also a term of A075252.
%C A092212 a(n) determines a 1-to-1 mapping from the terms of A092210 to the terms of A075252, the inverse of the mapping determined by A092211.
%C A092212 The 1-to-1 property of the mapping depends on the conjecture that the base-2 Reverse and Add! trajectory of each term of A092210 contains only a finite number of palindromes (cf. A092215).
%C A092212 Base-2 analog of A089494 (base 10) and A091677 (base 4).
%H A092212 <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%e A092212 A092210(3) = 64, the trajectory of 64 joins the trajectory of 89 at 48480, so a(3) = 89. A092210(5) = 98, the trajectory of 98 joins the trajectory of 3599 = A075252(16) at 401104704, so a(5) = 3599.
%t A092212 limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
%t A092212 utraj = NestList[# + IntegerReverse[#, 2] &, 1, limit];
%t A092212 A092210 = Flatten@{1, Select[Range[2, 266], (l =
%t A092212         Length@NestWhileList[# + IntegerReverse[#, 2] &, #, !
%t A092212             MemberQ[utraj, #] &, 1, limit];
%t A092212        utraj =
%t A092212         Union[utraj, NestList[# + IntegerReverse[#, 2] &, #, limit]];
%t A092212        l == limit + 1) &]};
%t A092212 A092212 = {};
%t A092212 For[i = 1, i <= Length@A092210, i++,
%t A092212 k = A092210[[i]];
%t A092212 itraj = NestList[# + IntegerReverse[#, 2] &, A092210[[i]], limit];
%t A092212 While[ktraj =
%t A092212    NestWhileList[# + IntegerReverse[#, 2] &,
%t A092212     k, # != IntegerReverse[#, 2] &, 1, limit];
%t A092212   PalindromeQ[k] || Length@ktraj != limit + 1 || ! IntersectingQ[itraj, ktraj], k++];
%t A092212 AppendTo[A092212, k]]; A092212 (* _Robert Price_, Nov 03 2019 *)
%Y A092212 Cf. A075252, A092210, A092211, A092215, A089494, A091677.
%K A092212 nonn,base,more
%O A092212 1,1
%A A092212 _Klaus Brockhaus_, Feb 25 2004
%E A092212 a(1) and a(3) corrected by _Robert Price_, Nov 06 2019