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%I #17 Nov 18 2019 01:27:14
%S 0,1,2,3,6,7,31,43,63,343
%N Numbers whose digits are in nondecreasing order in bases 4 and 5.
%C There are no more terms through 10^10000 (which is a 16610-digit number in base 4 and a 14307-digit number in base 5). But can it be proved that 343 is the final term of the sequence?
%e a(1) = 0 = 0_4 = 0_5
%e a(2) = 1 = 1_4 = 1_5
%e a(3) = 2 = 2_4 = 2_5
%e a(4) = 3 = 3_4 = 3_5
%e a(5) = 6 = 12_4 = 11_5
%e a(6) = 7 = 13_4 = 12_5
%e a(7) = 31 = 133_4 = 111_5
%e a(8) = 43 = 223_4 = 133_5
%e a(9) = 63 = 333_4 = 223_5
%e a(10) = 343 = 11113_4 = 2333_5
%o (PARI) isnondec(v) = (#v==0) || (#select(x->(x<0), vector(#v-1, k, v[k+1]-v[k])) == 0);
%o isok(n) = isnondec(digits(n, 4)) && isnondec(digits(n, 5)); \\ _Michel Marcus_, Nov 11 2019
%Y Intersection of A023746 (base 4) and A023747 (base 5).
%Y Numbers whose digits are in nondecreasing order in bases b and b+1: this sequence (b=4), A329295 (b=5), A329296 (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 09 2019
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