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.

A031990 Duplicate of A023747.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 18, 19, 24, 31, 32, 33, 34, 37, 38, 39, 43, 44, 49, 62, 63, 64, 68, 69, 74, 93, 94, 99, 124, 156, 157, 158, 159, 162, 163, 164, 168, 169, 174, 187, 188, 189, 193, 194, 199, 218, 219, 224, 249, 312, 313
Offset: 1

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Keywords

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

Original entry on oeis.org

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

Views

Author

Jon E. Schoenfield, Nov 09 2019

Keywords

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

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.
Showing 1-3 of 3 results.