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%I #4 Nov 18 2019 22:07:54
%S 0,1,2,3,4,5,6,7,10,11,12,13,14,15,20,21,22,23,30,31,91,92,93,94,95,
%T 101,102,103,111,151,182,183,222,223,293,294,295,303,365,366,367,374,
%U 375,822,823,831,951,1023,10023,14774,14775,14783,599551,608623,1203126,1203127,1203135
%N Numbers whose digits are in nondecreasing order in bases 8 and 9.
%C There are no more terms through 10^10000 (which is an 11074-digit number in base 8 and a 10480-digit number in base 9). But can it be proved that 1203135 is the final term of the sequence?
%e Sequence includes 8 terms that are 1-digit numbers in both bases, 12 that are 2-digit numbers in both bases, 23 that are 3-digit terms in both bases, and the following:
%e a(44) = 822 = 1466_8 = 1113_9
%e a(45) = 823 = 1467_8 = 1114_9
%e a(46) = 831 = 1477_8 = 1123_9
%e a(47) = 951 = 1667_8 = 1266_9
%e a(48) = 1023 = 1777_8 = 1356_9
%e a(49) = 10023 = 23447_8 = 14666_9
%e a(50) = 14774 = 34666_8 = 22235_9
%e a(51) = 14775 = 34667_8 = 22236_9
%e a(52) = 14783 = 34677_8 = 22245_9
%e a(53) = 599551 = 2222777_8 = 1113377_9
%e a(54) = 608623 = 2244557_8 = 1126777_9
%e a(55) = 1203126 = 4455666_8 = 2233336_9
%e a(56) = 1203127 = 4455667_8 = 2233337_9
%e a(57) = 1203135 = 4455677_8 = 2233346_9
%Y Intersection of A023750 (base 8) and A023751 (base 9). Numbers whose digits are in nondecreasing order in bases b and b+1: A329294 (b=4), A329295 (b=5), A329296 (b=6), A329297 (b=7), this sequence (b=8), A329299 (b=9). See A329300 for the (apparently) largest term of each of these sequences.
%K nonn,base
%O 1,3
%A _Jon E. Schoenfield_, Nov 17 2019
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