%I #6 Nov 18 2019 22:07:32
%S 0,1,2,3,4,5,8,9,10,11,16,17,57,58,59,65,89,130,131,172,173,179,1600,
%T 1601,3203
%N Numbers whose digits are in nondecreasing order in bases 6 and 7.
%C There are no more terms through 10^10000 (which is a 12851digit number in base 6 and an 11833digit number in base 7). But can it be proved that 3203 is the final term of the sequence?
%e a(1) = 0 = 0_6 = 0_7
%e a(2) = 1 = 1_6 = 1_7
%e a(3) = 2 = 2_6 = 2_7
%e a(4) = 3 = 3_6 = 3_7
%e a(5) = 4 = 4_6 = 4_7
%e a(6) = 5 = 5_6 = 5_7
%e a(7) = 8 = 12_6 = 11_7
%e a(8) = 9 = 13_6 = 12_7
%e a(9) = 10 = 14_6 = 13_7
%e a(10) = 11 = 15_6 = 14_7
%e a(11) = 16 = 24_6 = 22_7
%e a(12) = 17 = 25_6 = 23_7
%e a(13) = 57 = 133_6 = 111_7
%e a(14) = 58 = 134_6 = 112_7
%e a(15) = 59 = 135_6 = 113_7
%e a(16) = 65 = 145_6 = 122_7
%e a(17) = 89 = 225_6 = 155_7
%e a(18) = 130 = 334_6 = 244_7
%e a(19) = 131 = 335_6 = 245_7
%e a(20) = 172 = 444_6 = 334_7
%e a(21) = 173 = 445_6 = 335_7
%e a(22) = 179 = 455_6 = 344_7
%e a(23) = 1600 = 11224_6 = 4444_7
%e a(24) = 1601 = 11225_6 = 4445_7
%e a(25) = 3203 = 22455_6 = 12224_7
%Y 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 nonn,base
%O 1,3
%A _Jon E. Schoenfield_, Nov 17 2019
