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 1-6 of 6 results.

A050813 Numbers n not palindromic in any base b, 2 <= b <= 10.

Original entry on oeis.org

19, 39, 47, 53, 58, 69, 75, 76, 79, 84, 87, 90, 94, 95, 96, 102, 103, 106, 108, 110, 115, 116, 120, 122, 132, 133, 134, 137, 139, 140, 143, 144, 147, 149, 152, 155, 158, 159, 163, 167, 168, 169, 174, 175, 176, 177, 179, 180, 183, 184, 187, 188, 193, 196, 198
Offset: 1

Views

Author

Patrick De Geest, Oct 15 1999

Keywords

Links

Crossrefs

Cf. A050812, A047811, A016038.
Cf. A214423, A214424, A214425, A214426 (palindromic in 1-4 bases).

Programs

  • Mathematica
    n = -1; t = {}; While[Length[t] < 100, n++; If[Count[Table[s = IntegerDigits[n, m]; s == Reverse[s], {m, 2, 10}], True] == 0, AppendTo[t, n]]]; t (* T. D. Noe, Jul 18 2012 *)

Formula

A050812(n) = 0.

A214423 Numbers n palindromic in only one base b, 2 <= b <= 10.

Original entry on oeis.org

11, 12, 13, 14, 22, 23, 25, 29, 30, 32, 34, 35, 37, 38, 41, 42, 43, 44, 48, 49, 54, 56, 59, 60, 61, 62, 64, 66, 68, 70, 71, 72, 74, 77, 81, 83, 86, 89, 97, 101, 112, 113, 117, 118, 123, 124, 125, 126, 128, 131, 136, 138, 145, 146, 148, 153, 156, 157, 161
Offset: 1

Views

Author

T. D. Noe, Jul 18 2012

Keywords

Comments

The base for which n is a palindrome is given in A214427.

Examples

			11 is palindromic only in base 10.

Links

Crossrefs

Cf. A050813, A214424, A214425, A214426 (palindromic in 0, 2-4 bases)

Programs

  • Mathematica
    n = -1; t = {}; While[Length[t] < 100, n++; If[Count[Table[s = IntegerDigits[n, m]; s == Reverse[s], {m, 2, 10}], True] == 1, AppendTo[t, n]]]; t

Formula

A050812(n) = 1.

A214425 Numbers n palindromic in exactly three bases b, 2 <= b <= 10.

Original entry on oeis.org

9, 10, 21, 40, 55, 63, 65, 80, 85, 100, 130, 154, 164, 178, 191, 195, 203, 235, 242, 255, 257, 273, 282, 292, 300, 325, 328, 341, 400, 455, 585, 656, 819, 910, 2709, 4095, 4097, 4161, 6643, 8200, 12291, 12483, 14762, 20485, 20805, 21525, 21845, 32152, 53235
Offset: 1

Views

Author

T. D. Noe, Jul 18 2012

Keywords

Comments

In the first 1234 terms, only 28 of the possible 84 triples of bases occur. Does every triple occur eventually? - T. D. Noe, Aug 17 2012
See A238893 for the three bases. By far, the most common bases are (2,4,8). - T. D. Noe, Mar 07 2014 (exception are in A260184. - Giovanni Resta and Robert G. Wilson v, Jul 17 2015).

Examples

			10 is palindromic in bases 3, 4, and 9.
273 is in the sequence because 100010001_2 = 101010_3 = 10101_4 = 2043_5 = 1133_6 = 540_7 = 421_8 = 333_9 = 273_10 and three of the bases, namely 2, 4 & 9, yield palindromes. - _Giovanni Resta_ and _Robert G. Wilson v_, Jul 17 2015

Links

Crossrefs

Cf. A050813, A214423, A214424, A214426 (palindromic in 0-2 and 4 bases).

Programs

  • Mathematica
    n = -1; t = {}; While[Length[t] < 100, n++; If[Count[Table[s = IntegerDigits[n, m]; s == Reverse[s], {m, 2, 10}], True] == 3, AppendTo[t, n]]]; t

Formula

A050812(n) = 3.
The intersection of A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955 & A002113 which yields just three members. - Giovanni Resta and Robert G. Wilson v, Jul 17 2015

A214424 Numbers that are palindromic in exactly two bases b, 2 <= b <= 10.

Original entry on oeis.org

15, 16, 17, 18, 20, 24, 26, 27, 28, 31, 33, 36, 45, 46, 50, 51, 52, 57, 67, 73, 78, 82, 88, 91, 92, 93, 98, 99, 104, 105, 107, 109, 111, 114, 119, 127, 129, 135, 141, 142, 150, 151, 160, 170, 171, 173, 182, 185, 186, 200, 209, 212, 215, 219, 227, 246, 252
Offset: 1

Views

Author

T. D. Noe, Jul 18 2012

Keywords

Comments

Every pair of bases occurs. The pair (2,3), for the number a(732) = 1422773, is the last to occur. Note that 1422773 = 101011011010110110101(2) = 2200021200022(3).
See A238338 for the pairs of bases. - T. D. Noe, Mar 07 2014

Examples

			15 is palindromic in bases 2 and 4: 15 = 1111_2 = 33_4.

Links

Crossrefs

Cf. A050813, A214423, A214425, A214426 (palindromic in 0-1 and 3-4 bases).

Programs

  • Mathematica
    n = -1; t = {}; While[Length[t] < 100, n++; If[Count[Table[s = IntegerDigits[n, m]; s == Reverse[s], {m, 2, 10}], True] == 2, AppendTo[t, n]]]; t
  • PARI
    pal(v)=v==Vecrev(v)
is(n)=sum(b=2,10,pal(digits(n,b)))==2 \\ Charles R Greathouse IV, Mar 05 2014

Formula

A050812(a(n)) = 2.

A260184 Numbers n written in base 10 that are palindromic in exactly three bases b, 2 <= b <= 10 and not simultaneously bases 2, 4 and 8.

Original entry on oeis.org

9, 10, 21, 40, 55, 80, 85, 100, 130, 154, 164, 178, 191, 203, 235, 242, 255, 257, 273, 282, 292, 300, 328, 400, 455, 585, 656, 819, 910, 2709, 6643, 8200, 14762, 32152, 53235, 74647, 428585, 532900, 1181729, 1405397, 4210945, 5259525, 27711772, 719848917, 43253138565
Offset: 1

Views

Author

Giovanni Resta and Robert G. Wilson v, Jul 17 2015

Keywords

Examples

			273 is in the sequence because 100010001_2 = 101010_3 = 10101_4 = 2043_5 = 1133_6 = 540_7 = 421_8 = 333_9 = 273_10 and three of the bases, namely 2, 4 & 9, yield palindromes.

Links

Crossrefs

Cf. A214426, A214425.

Programs

  • Mathematica
    (* see A214425 and set all terms as lst, then *)
gQ[n_] := Count[ palQ[n,#] & /@ {2, 4, 8}, True];
Select[ lst, gQ[#] != 3 &]

Formula

The intersection of A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955 & A002113 which yields just three members, not simultaneously bases 2, 4 and 8.

A214422 Least number k > 9 that is palindromic in exactly n bases b, with 2 <= b <= 10.

Original entry on oeis.org

19, 11, 15, 10, 121
Offset: 0

Views

Author

T. D. Noe, Jul 18 2012

Keywords

Comments

There are no other terms < 10^12. The ultimate goal is to find (probably a very large) k that is palindromic in all 9 bases 2 to 10.

Examples

			19 is not palindromic in bases 2 to 10.
11 is palindromic in base 10.
15 is palindromic in bases 2 and 4.
10 is palindromic in bases 3, 4, and 9.
121 is palindromic in bases 3, 7, 8, and 10.

Crossrefs

Cf. A050813, A214423, A214424, A214425, A214426 (palindromic in 0-4 bases).
Showing 1-6 of 6 results.

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