

A092212


a(n) = smallest nonpalindromic k such that the base2 Reverse and Add! trajectory of k is palindromefree and joins the trajectory of A092210(n).


2




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) determines a 1to1 mapping from the terms of A092210 to the terms of A075252, the inverse of the mapping determined by A092211.
The 1to1 property of the mapping depends on the conjecture that the base2 Reverse and Add! trajectory of each term of A092210 contains only a finite number of palindromes (cf. A092215).


LINKS



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) &]};
For[i = 1, i <= Length@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++];


CROSSREFS



KEYWORD

nonn,base,more


AUTHOR



EXTENSIONS



STATUS

approved



