A329295 Numbers whose digits are in nondecreasing order in bases 5 and 6.

0, 1, 2, 3, 4, 7, 8, 9, 14, 43, 44, 64, 93, 94, 784, 1562, 1563, 1564, 1569, 1599, 3124, 9374

Offset: 1

Author

Jon E. Schoenfield, Nov 17 2019

Keywords

• nonn
• base

Comments

There are no more terms through 10^10000 (which is a 14307-digit number in base 5 and a 12851-digit number in base 6). But can it be proved that 9374 is the final term of the sequence?

Examples

			a(1)  =    0 =      0_5 =      0_6
a(2)  =    1 =      1_5 =      1_6
a(3)  =    2 =      2_5 =      2_6
a(4)  =    3 =      3_5 =      3_6
a(5)  =    4 =      4_5 =      4_6
a(6)  =    7 =     12_5 =     11_6
a(7)  =    8 =     13_5 =     12_6
a(8)  =    9 =     14_5 =     13_6
a(9)  =   14 =     24_5 =     22_6
a(10) =   43 =    133_5 =    111_6
a(11) =   44 =    134_5 =    112_6
a(12) =   64 =    224_5 =    144_6
a(13) =   93 =    333_5 =    233_6
a(14) =   94 =    334_5 =    234_6
a(15) =  784 =  11114_5 =   3344_6
a(16) = 1562 =  22222_5 =  11122_6
a(17) = 1563 =  22223_5 =  11123_6
a(18) = 1564 =  22224_5 =  11124_6
a(19) = 1569 =  22234_5 =  11133_6
a(20) = 1599 =  22344_5 =  11223_6
a(21) = 3124 =  44444_5 =  22244_6
a(22) = 9374 = 244444_5 = 111222_6
		

Crossrefs

Intersection of A023747 (base 5) and A023748 (base 6).

Numbers whose digits are in nondecreasing order in bases b and b+1: A329294 (b=4), this sequence (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.