A092212 - OEIS

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).

26, 65649, 89, 4193, 3599, 775, 68076, 2173

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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]];