cp's OEIS Frontend

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

%I A329296 #6 Nov 18 2019 22:07:32
%S A329296 0,1,2,3,4,5,8,9,10,11,16,17,57,58,59,65,89,130,131,172,173,179,1600,
%T A329296 1601,3203
%N A329296 Numbers whose digits are in nondecreasing order in bases 6 and 7.
%C A329296 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?
%e A329296 a(1)  =    0 =     0_6 =     0_7
%e A329296 a(2)  =    1 =     1_6 =     1_7
%e A329296 a(3)  =    2 =     2_6 =     2_7
%e A329296 a(4)  =    3 =     3_6 =     3_7
%e A329296 a(5)  =    4 =     4_6 =     4_7
%e A329296 a(6)  =    5 =     5_6 =     5_7
%e A329296 a(7)  =    8 =    12_6 =    11_7
%e A329296 a(8)  =    9 =    13_6 =    12_7
%e A329296 a(9)  =   10 =    14_6 =    13_7
%e A329296 a(10) =   11 =    15_6 =    14_7
%e A329296 a(11) =   16 =    24_6 =    22_7
%e A329296 a(12) =   17 =    25_6 =    23_7
%e A329296 a(13) =   57 =   133_6 =   111_7
%e A329296 a(14) =   58 =   134_6 =   112_7
%e A329296 a(15) =   59 =   135_6 =   113_7
%e A329296 a(16) =   65 =   145_6 =   122_7
%e A329296 a(17) =   89 =   225_6 =   155_7
%e A329296 a(18) =  130 =   334_6 =   244_7
%e A329296 a(19) =  131 =   335_6 =   245_7
%e A329296 a(20) =  172 =   444_6 =   334_7
%e A329296 a(21) =  173 =   445_6 =   335_7
%e A329296 a(22) =  179 =   455_6 =   344_7
%e A329296 a(23) = 1600 = 11224_6 =  4444_7
%e A329296 a(24) = 1601 = 11225_6 =  4445_7
%e A329296 a(25) = 3203 = 22455_6 = 12224_7
%Y A329296 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.
%K A329296 nonn,base
%O A329296 1,3
%A A329296 _Jon E. Schoenfield_, Nov 17 2019