%I #21 Aug 12 2022 09:23:18
%S 178,154593982,3360633,0,0,0
%N a(n) is the smallest number that is a (2n+1)-digit palindrome in three consecutive integer bases, or 0 if no such number exists.
%C It is conjectured that a(n)=0 for all n>=4. - _Matej Veselovac_, Mar 25 2020
%H Max Alekseyev, <a href="https://math.stackexchange.com/a/3382910/318073">Generalized system and related problems</a>, Mathematics Stack Exchange, Oct 06 2019
%e a(1)=178 is the smallest number that is a 3-digit palindrome in three consecutive integer bases: 178 = 454_6 = 343_7 = 262_8.
%e a(2)=154593982 is the smallest number that is a 5-digit palindrome in three consecutive integer bases: 154593982 = (37,31,22,31,37)_45 = (34,24,11,24,34)_46 = (31,32,0,32,31)_47.
%e a(3)=3360633 is the smallest number that is a 7-digit palindrome in three consecutive integer bases: 3360633 = 6281826_9 = 3360633_10 = 1995991_11.
%Y Cf. A279093, A327810.
%K nonn,base,hard,more
%O 1,1
%A _Jon E. Schoenfield_, Mar 24 2019
%E a(4)-a(6) from _Max Alekseyev_, Jun 14 2020