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.
EXAMPLE
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++];
CROSSREFS
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