A329296 Numbers whose digits are in nondecreasing order in bases 6 and 7.

0, 1, 2, 3, 4, 5, 8, 9, 10, 11, 16, 17, 57, 58, 59, 65, 89, 130, 131, 172, 173, 179, 1600, 1601, 3203

Offset

1,3

Comments

There are no more terms through 10^10000 (which is a 12851-digit number in base 6 and an 11833-digit number in base 7). But can it be proved that 3203 is the final term of the sequence?

Links

Table of n, a(n) for n=1..25.

Example

a(1)  =    0 =     0_6 =     0_7
a(2)  =    1 =     1_6 =     1_7
a(3)  =    2 =     2_6 =     2_7
a(4)  =    3 =     3_6 =     3_7
a(5)  =    4 =     4_6 =     4_7
a(6)  =    5 =     5_6 =     5_7
a(7)  =    8 =    12_6 =    11_7
a(8)  =    9 =    13_6 =    12_7
a(9)  =   10 =    14_6 =    13_7
a(10) =   11 =    15_6 =    14_7
a(11) =   16 =    24_6 =    22_7
a(12) =   17 =    25_6 =    23_7
a(13) =   57 =   133_6 =   111_7
a(14) =   58 =   134_6 =   112_7
a(15) =   59 =   135_6 =   113_7
a(16) =   65 =   145_6 =   122_7
a(17) =   89 =   225_6 =   155_7
a(18) =  130 =   334_6 =   244_7
a(19) =  131 =   335_6 =   245_7
a(20) =  172 =   444_6 =   334_7
a(21) =  173 =   445_6 =   335_7
a(22) =  179 =   455_6 =   344_7
a(23) = 1600 = 11224_6 =  4444_7
a(24) = 1601 = 11225_6 =  4445_7
a(25) = 3203 = 22455_6 = 12224_7

Crossrefs

Intersection of A023748 (base 6) and A023749 (base 7). Numbers whose digits are in nondecreasing order in bases b and b+1: A329294 (b=4), A329295 (b=5), this sequence (b=6), A329297 (b=7), A329298 (b=8), A329299 (b=9). See A329300 for the (apparently) largest term of each of these sequences.

Sequence in context: A032844 A023775 A363235 * A356713 A032867 A031999

Adjacent sequences: A329293 A329294 A329295 * A329297 A329298 A329299

Keyword

nonn,base

Author

Jon E. Schoenfield, Nov 17 2019

Status

approved