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.

Showing 1-3 of 3 results.

A031992 Duplicate of A023749.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 24, 25, 26, 27, 32, 33, 34, 40, 41, 48, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 73, 74, 75, 76, 81, 82, 83, 89, 90, 97, 114, 115, 116, 117, 118, 122, 123, 124, 125, 130, 131, 132
Offset: 1

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Keywords

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

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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.

A329297 Numbers whose digits are in nondecreasing order in bases 7 and 8.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 18, 19, 20, 27, 73, 74, 75, 76, 82, 83, 118, 146, 173, 174, 228, 229, 230, 237, 293, 587, 685, 804, 2925, 14062, 42131, 42132, 42139, 411942
Offset: 1

Views

Author

Jon E. Schoenfield, Nov 17 2019

Keywords

Comments

There are no more terms through 10^10000 (which is an 11833-digit number in base 7 and an 11074-digit number in base 8). But can it be proved that 411942 is the final term of the sequence?

Examples

			Sequence includes 7 terms that are 1-digit numbers in both bases, 9 terms that are 2-digit numbers in both bases, and the following:
  a(17) =     73 =     133_7 =     111_8
  a(18) =     74 =     134_7 =     112_8
  a(19) =     75 =     135_7 =     113_8
  a(20) =     76 =     136_7 =     114_8
  a(21) =     82 =     145_7 =     122_8
  a(22) =     83 =     146_7 =     123_8
  a(23) =    118 =     226_7 =     166_8
  a(24) =    146 =     266_7 =     222_8
  a(25) =    173 =     335_7 =     255_8
  a(26) =    174 =     336_7 =     256_8
  a(27) =    228 =     444_7 =     344_8
  a(28) =    229 =     445_7 =     345_8
  a(29) =    230 =     446_7 =     346_8
  a(30) =    237 =     456_7 =     355_8
  a(31) =    293 =     566_7 =     445_8
  a(32) =    587 =    1466_7 =    1113_8
  a(33) =    685 =    1666_7 =    1255_8
  a(34) =    804 =    2226_7 =    1444_8
  a(35) =   2925 =   11346_7 =    5555_8
  a(36) =  14062 =   55666_7 =   33356_8
  a(37) =  42131 =  233555_7 =  122223_8
  a(38) =  42132 =  233556_7 =  122224_8
  a(39) =  42139 =  233566_7 =  122233_8
  a(40) = 411942 = 3333666_7 = 1444446_8
		

Crossrefs

Intersection of A023749 (base 7) and A023750 (base 8). Numbers whose digits are in nondecreasing order in bases b and b+1: A329294 (b=4), A329295 (b=5), A329296 (b=6), this sequence (b=7), A329298 (b=8), A329299 (b=9). See A329300 for the (apparently) largest term of each of these sequences.
Showing 1-3 of 3 results.