login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A323742
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.
1
178, 154593982, 3360633, 0, 0, 0
OFFSET
1,1
COMMENTS
It is conjectured that a(n)=0 for all n>=4. - Matej Veselovac, Mar 25 2020
LINKS
Max Alekseyev, Generalized system and related problems, Mathematics Stack Exchange, Oct 06 2019
EXAMPLE
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.
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.
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.
CROSSREFS
Sequence in context: A189440 A163730 A157842 * A273550 A053017 A140026
KEYWORD
nonn,base,hard,more
AUTHOR
Jon E. Schoenfield, Mar 24 2019
EXTENSIONS
a(4)-a(6) from Max Alekseyev, Jun 14 2020
STATUS
approved