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 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). 2
 26, 65649, 89, 4193, 3599, 775, 68076, 2173 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. 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. 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. 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). Base-2 analog of A089494 (base 10) and A091677 (base 4). LINKS Table of n, a(n) for n=1..8. Index entries for sequences related to Reverse and Add! EXAMPLE 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. MATHEMATICA limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *) utraj = NestList[# + IntegerReverse[#, 2] &, 1, limit]; A092210 = Flatten@{1, Select[Range[2, 266], (l = Length@NestWhileList[# + IntegerReverse[#, 2] &, #, ! MemberQ[utraj, #] &, 1, limit]; utraj = Union[utraj, NestList[# + IntegerReverse[#, 2] &, #, limit]]; l == limit + 1) &]}; A092212 = {}; For[i = 1, i <= Length@A092210, i++, k = A092210[[i]]; itraj = NestList[# + IntegerReverse[#, 2] &, A092210[[i]], limit]; While[ktraj = NestWhileList[# + IntegerReverse[#, 2] &, k, # != IntegerReverse[#, 2] &, 1, limit]; PalindromeQ[k] || Length@ktraj != limit + 1 || ! IntersectingQ[itraj, ktraj], k++]; AppendTo[A092212, k]]; A092212 (* Robert Price, Nov 03 2019 *) CROSSREFS Cf. A075252, A092210, A092211, A092215, A089494, A091677. Sequence in context: A302396 A208186 A316677 * A365983 A265959 A112946 Adjacent sequences: A092209 A092210 A092211 * A092213 A092214 A092215 KEYWORD nonn,base,more AUTHOR Klaus Brockhaus, Feb 25 2004 EXTENSIONS a(1) and a(3) corrected by Robert Price, Nov 06 2019 STATUS approved

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Last modified May 26 21:09 EDT 2024. Contains 372844 sequences. (Running on oeis4.)