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

1,3

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?

Links

Table of n, a(n) for n=1..40.

Example

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.

Sequence in context: A330029 A368841 A201992 * A236562 A377333 A157189

Adjacent sequences: A329294 A329295 A329296 * A329298 A329299 A329300

Keyword

nonn,base

Author

Jon E. Schoenfield, Nov 17 2019

Status

approved