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.

Previous Showing 31-33 of 33 results.

A043267 Sum of the digits of the n-th base 8 palindrome.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 2, 4, 6, 8, 10, 12, 14, 2, 3, 4, 5, 6, 7, 8, 9, 4, 5, 6, 7, 8, 9, 10, 11, 6, 7, 8, 9, 10, 11, 12, 13, 8, 9, 10, 11, 12, 13, 14, 15, 10, 11, 12, 13, 14, 15, 16, 17, 12, 13, 14, 15, 16, 17, 18, 19, 14, 15, 16, 17, 18, 19, 20, 21
Offset: 1

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Author

Keywords

Crossrefs

A029803 (base 8 palindromes)

A319585 Numbers in base 10 that are palindromic in bases 2, 8, and 16.

Original entry on oeis.org

0, 1, 3, 5, 7, 9, 3951, 4095, 4097, 12291, 20485, 21845, 28679, 30039, 36873, 16187247, 16777215, 16777217, 16781313, 50331651, 50343939, 83886085, 83894277, 83906565, 83914757, 89458005, 89466197, 89478485, 89486677, 117440519, 117448711, 117460999
Offset: 1

Views

Author

Jeremias M. Gomes, Sep 23 2018

Keywords

Comments

Intersection of A006995, A029803, and A029730.

Examples

			16187247 = 111101101111111101101111_2 = 75577557_8 = F6FF6F_16.
		

Crossrefs

Cf. A006995 (base 2), A029803 (base 8), and A029730 (base 16).

Programs

  • Magma
    [n: n in [0..2*10^7] | Intseq(n, 2) eq Reverse(Intseq(n, 2)) and Intseq(n, 8) eq Reverse(Intseq(n, 8)) and Intseq(n, 16) eq Reverse(Intseq(n, 16))]; // Vincenzo Librandi, Sep 24 2018
  • Mathematica
    palQ[n_, b_] := PalindromeQ[IntegerDigits[n, b]];
    Reap[Do[If[palQ[n, 2] && palQ[n, 8] && palQ[n, 16], Print[n]; Sow[n]], {n, 0, 10^6}]][[2, 1]] (* Jean-François Alcover, Sep 25 2018 *)
  • Sage
    [n for n in (0..10000) if Word(n.digits(2)).is_palindrome() and Word(n.digits(8)).is_palindrome() and Word(n.digits(16)).is_palindrome()]
    

A319609 Numbers in base 10 that are palindromic in bases 4, 8 and 16.

Original entry on oeis.org

0, 1, 2, 3, 5, 170, 4095, 4097, 8194, 12291, 20485, 21845, 696490, 699050, 16777215, 16777217, 16781313, 16785409, 16789505, 33554434, 33558530, 33562626, 33566722, 50331651, 50335747, 50339843, 50343939, 83886085, 83906565, 89458005, 89478485
Offset: 1

Views

Author

Jeremias M. Gomes, Sep 24 2018

Keywords

Examples

			170 = 2222_4 = 252_8 = AA_16. Hence 170 is in the sequence.
		

Crossrefs

Intersection of A014192, A029803 and A029730.

Programs

  • Magma
    [n: n in [0..2*10^7] | Intseq(n, 4) eq Reverse(Intseq(n, 4)) and Intseq(n, 8) eq Reverse(Intseq(n, 8)) and Intseq(n, 16) eq Reverse(Intseq(n, 16))]; // Vincenzo Librandi, Sep 24 2018
  • Mathematica
    palQ[n_, b_] := PalindromeQ[IntegerDigits[n, b]];
    Reap[Do[If[palQ[n, 4] && palQ[n, 8] && palQ[n, 16], Print[n]; Sow[n]], {n, 0, 10^6}]][[2, 1]] (* Jean-François Alcover, Sep 25 2018 *)
  • Sage
    [n for n in (0..100000) if Word(n.digits(4)).is_palindrome() and Word(n.digits(8)).is_palindrome() and Word(n.digits(16)).is_palindrome()]
    
Previous Showing 31-33 of 33 results.