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

1,3

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?

Links

Table of n, a(n) for n=1..57.

Example

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.

Sequence in context: A032879 A032846 A023777 * A074946 A279455 A050687

Adjacent sequences: A329295 A329296 A329297 * A329299 A329300 A329301

Keyword

nonn,base

Author

Jon E. Schoenfield, Nov 17 2019

Status

approved