A329297 Numbers whose digits are in nondecreasing order in bases 7 and 8.

0, 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 18, 19, 20, 27, 73, 74, 75, 76, 82, 83, 118, 146, 173, 174, 228, 229, 230, 237, 293, 587, 685, 804, 2925, 14062, 42131, 42132, 42139, 411942

Offset: 1

Author

Jon E. Schoenfield, Nov 17 2019

Keywords

• nonn
• base

Comments

There are no more terms through 10^10000 (which is an 11833-digit number in base 7 and an 11074-digit number in base 8). But can it be proved that 411942 is the final term of the sequence?

Examples

			Sequence includes 7 terms that are 1-digit numbers in both bases, 9 terms that are 2-digit numbers in both bases, and the following:
  a(17) =     73 =     133_7 =     111_8
  a(18) =     74 =     134_7 =     112_8
  a(19) =     75 =     135_7 =     113_8
  a(20) =     76 =     136_7 =     114_8
  a(21) =     82 =     145_7 =     122_8
  a(22) =     83 =     146_7 =     123_8
  a(23) =    118 =     226_7 =     166_8
  a(24) =    146 =     266_7 =     222_8
  a(25) =    173 =     335_7 =     255_8
  a(26) =    174 =     336_7 =     256_8
  a(27) =    228 =     444_7 =     344_8
  a(28) =    229 =     445_7 =     345_8
  a(29) =    230 =     446_7 =     346_8
  a(30) =    237 =     456_7 =     355_8
  a(31) =    293 =     566_7 =     445_8
  a(32) =    587 =    1466_7 =    1113_8
  a(33) =    685 =    1666_7 =    1255_8
  a(34) =    804 =    2226_7 =    1444_8
  a(35) =   2925 =   11346_7 =    5555_8
  a(36) =  14062 =   55666_7 =   33356_8
  a(37) =  42131 =  233555_7 =  122223_8
  a(38) =  42132 =  233556_7 =  122224_8
  a(39) =  42139 =  233566_7 =  122233_8
  a(40) = 411942 = 3333666_7 = 1444446_8
		

Crossrefs

Intersection of A023749 (base 7) and A023750 (base 8). Numbers whose digits are in nondecreasing order in bases b and b+1: A329294 (b=4), A329295 (b=5), A329296 (b=6), this sequence (b=7), A329298 (b=8), A329299 (b=9). See A329300 for the (apparently) largest term of each of these sequences.