cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

Jon E. Schoenfield, Nov 17 2019

Keywords

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.

A329296 Numbers whose digits are in nondecreasing order in bases 6 and 7.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 8, 9, 10, 11, 16, 17, 57, 58, 59, 65, 89, 130, 131, 172, 173, 179, 1600, 1601, 3203
Offset: 1

Views

Author

Jon E. Schoenfield, Nov 17 2019

Keywords

Comments

There are no more terms through 10^10000 (which is a 12851-digit number in base 6 and an 11833-digit number in base 7). But can it be proved that 3203 is the final term of the sequence?

Examples

			a(1)  =    0 =     0_6 =     0_7
a(2)  =    1 =     1_6 =     1_7
a(3)  =    2 =     2_6 =     2_7
a(4)  =    3 =     3_6 =     3_7
a(5)  =    4 =     4_6 =     4_7
a(6)  =    5 =     5_6 =     5_7
a(7)  =    8 =    12_6 =    11_7
a(8)  =    9 =    13_6 =    12_7
a(9)  =   10 =    14_6 =    13_7
a(10) =   11 =    15_6 =    14_7
a(11) =   16 =    24_6 =    22_7
a(12) =   17 =    25_6 =    23_7
a(13) =   57 =   133_6 =   111_7
a(14) =   58 =   134_6 =   112_7
a(15) =   59 =   135_6 =   113_7
a(16) =   65 =   145_6 =   122_7
a(17) =   89 =   225_6 =   155_7
a(18) =  130 =   334_6 =   244_7
a(19) =  131 =   335_6 =   245_7
a(20) =  172 =   444_6 =   334_7
a(21) =  173 =   445_6 =   335_7
a(22) =  179 =   455_6 =   344_7
a(23) = 1600 = 11224_6 =  4444_7
a(24) = 1601 = 11225_6 =  4445_7
a(25) = 3203 = 22455_6 = 12224_7

Crossrefs

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.
Showing 1-2 of 2 results.

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