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.

178, 154593982, 3360633, 0, 0, 0

Offset: 1

Author

Jon E. Schoenfield, Mar 24 2019

Keywords

• nonn
• base
• hard
• more

Comments

It is conjectured that a(n)=0 for all n>=4. - Matej Veselovac, Mar 25 2020

Examples

			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.
		

Links

• Max Alekseyev, Generalized system and related problems, Mathematics Stack Exchange, Oct 06 2019

Crossrefs

Cf. A279093, A327810.

Extensions

a(4)-a(6) from Max Alekseyev, Jun 14 2020