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