A329298 Numbers whose digits are in nondecreasing order in bases 8 and 9.

0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 30, 31, 91, 92, 93, 94, 95, 101, 102, 103, 111, 151, 182, 183, 222, 223, 293, 294, 295, 303, 365, 366, 367, 374, 375, 822, 823, 831, 951, 1023, 10023, 14774, 14775, 14783, 599551, 608623, 1203126, 1203127, 1203135

Offset: 1

Author

Jon E. Schoenfield, Nov 17 2019

Keywords

• nonn
• base

Comments

There are no more terms through 10^10000 (which is an 11074-digit number in base 8 and a 10480-digit number in base 9). But can it be proved that 1203135 is the final term of the sequence?

Examples

			Sequence includes 8 terms that are 1-digit numbers in both bases, 12 that are 2-digit numbers in both bases, 23 that are 3-digit terms in both bases, and the following:
  a(44) =     822 =    1466_8 =    1113_9
  a(45) =     823 =    1467_8 =    1114_9
  a(46) =     831 =    1477_8 =    1123_9
  a(47) =     951 =    1667_8 =    1266_9
  a(48) =    1023 =    1777_8 =    1356_9
  a(49) =   10023 =   23447_8 =   14666_9
  a(50) =   14774 =   34666_8 =   22235_9
  a(51) =   14775 =   34667_8 =   22236_9
  a(52) =   14783 =   34677_8 =   22245_9
  a(53) =  599551 = 2222777_8 = 1113377_9
  a(54) =  608623 = 2244557_8 = 1126777_9
  a(55) = 1203126 = 4455666_8 = 2233336_9
  a(56) = 1203127 = 4455667_8 = 2233337_9
  a(57) = 1203135 = 4455677_8 = 2233346_9
		

Crossrefs

Intersection of A023750 (base 8) and A023751 (base 9). Numbers whose digits are in nondecreasing order in bases b and b+1: A329294 (b=4), A329295 (b=5), A329296 (b=6), A329297 (b=7), this sequence (b=8), A329299 (b=9). See A329300 for the (apparently) largest term of each of these sequences.