A329294 Numbers whose digits are in nondecreasing order in bases 4 and 5.

0, 1, 2, 3, 6, 7, 31, 43, 63, 343

Offset: 1

Author

Jon E. Schoenfield, Nov 09 2019

Keywords

• nonn
• base

Comments

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?

Examples

			a(1)  =   0 =     0_4 =    0_5
a(2)  =   1 =     1_4 =    1_5
a(3)  =   2 =     2_4 =    2_5
a(4)  =   3 =     3_4 =    3_5
a(5)  =   6 =    12_4 =   11_5
a(6)  =   7 =    13_4 =   12_5
a(7)  =  31 =   133_4 =  111_5
a(8)  =  43 =   223_4 =  133_5
a(9)  =  63 =   333_4 =  223_5
a(10) = 343 = 11113_4 = 2333_5
		

Crossrefs

Intersection of A023746 (base 4) and A023747 (base 5).

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.

Programs

PARI

isnondec(v) = (#v==0) || (#select(x->(x<0), vector(#v-1, k, v[k+1]-v[k])) == 0);
isok(n) = isnondec(digits(n, 4)) && isnondec(digits(n, 5)); \\ Michel Marcus, Nov 11 2019