cp's OEIS Frontend

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

%I A329297 #5 Nov 18 2019 22:07:38
%S A329297 0,1,2,3,4,5,6,9,10,11,12,13,18,19,20,27,73,74,75,76,82,83,118,146,
%T A329297 173,174,228,229,230,237,293,587,685,804,2925,14062,42131,42132,42139,
%U A329297 411942
%N A329297 Numbers whose digits are in nondecreasing order in bases 7 and 8.
%C A329297 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?
%e A329297 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:
%e A329297   a(17) =     73 =     133_7 =     111_8
%e A329297   a(18) =     74 =     134_7 =     112_8
%e A329297   a(19) =     75 =     135_7 =     113_8
%e A329297   a(20) =     76 =     136_7 =     114_8
%e A329297   a(21) =     82 =     145_7 =     122_8
%e A329297   a(22) =     83 =     146_7 =     123_8
%e A329297   a(23) =    118 =     226_7 =     166_8
%e A329297   a(24) =    146 =     266_7 =     222_8
%e A329297   a(25) =    173 =     335_7 =     255_8
%e A329297   a(26) =    174 =     336_7 =     256_8
%e A329297   a(27) =    228 =     444_7 =     344_8
%e A329297   a(28) =    229 =     445_7 =     345_8
%e A329297   a(29) =    230 =     446_7 =     346_8
%e A329297   a(30) =    237 =     456_7 =     355_8
%e A329297   a(31) =    293 =     566_7 =     445_8
%e A329297   a(32) =    587 =    1466_7 =    1113_8
%e A329297   a(33) =    685 =    1666_7 =    1255_8
%e A329297   a(34) =    804 =    2226_7 =    1444_8
%e A329297   a(35) =   2925 =   11346_7 =    5555_8
%e A329297   a(36) =  14062 =   55666_7 =   33356_8
%e A329297   a(37) =  42131 =  233555_7 =  122223_8
%e A329297   a(38) =  42132 =  233556_7 =  122224_8
%e A329297   a(39) =  42139 =  233566_7 =  122233_8
%e A329297   a(40) = 411942 = 3333666_7 = 1444446_8
%Y A329297 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.
%K A329297 nonn,base
%O A329297 1,3
%A A329297 _Jon E. Schoenfield_, Nov 17 2019