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 1-4 of 4 results.

A071272 Palindromes in A066492.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 101, 111, 121, 131, 141, 151, 161, 171, 181, 202, 212, 222, 232, 242, 252, 262, 272, 303, 313, 323, 333, 343, 353, 363, 404, 414, 424, 434, 444, 454, 505, 515, 525, 535, 545, 606, 616, 626, 636, 707, 717, 727, 808, 818, 909, 10001
Offset: 1

Views

Author

Amarnath Murthy, Jun 07 2002

Keywords

Crossrefs

Extensions

More terms from Sean A. Irvine, Jul 07 2024

A071271 Duplicate of A066492.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 91, 101, 111, 121, 131, 141, 151, 161, 171, 181, 182, 192
Offset: 1

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Author

Keywords

A056524 Palindromes with even number of digits.

Original entry on oeis.org

11, 22, 33, 44, 55, 66, 77, 88, 99, 1001, 1111, 1221, 1331, 1441, 1551, 1661, 1771, 1881, 1991, 2002, 2112, 2222, 2332, 2442, 2552, 2662, 2772, 2882, 2992, 3003, 3113, 3223, 3333, 3443, 3553, 3663, 3773, 3883, 3993, 4004, 4114, 4224, 4334, 4444, 4554
Offset: 1

Views

Author

Henry Bottomley, Jun 16 2000

Keywords

Comments

Concatenation of n with reverse of n (keeping leading zeros in the reverse).
A178788(a(n)) = 0 for n > 1. - Reinhard Zumkeller, Jun 30 2010
All of the terms are divisible by eleven. - James Burling, Aug 08 2014

Crossrefs

Cf. A110745 (permutation).

Programs

  • Haskell
    a056524 n = a056524_list !! (n-1)
    a056524_list = [read (ns ++ reverse ns) :: Integer |
                    n <- [0..], let ns = show n]
    -- Reinhard Zumkeller, Dec 28 2011
    
  • Mathematica
    d[n_]:=IntegerDigits[n]; Table[FromDigits[Join[x=d[n],Reverse[x]]],{n,45}] (* Jayanta Basu, May 29 2013 *)
    Select[Flatten[Table[Range[10^n,10^(n+1)-1],{n,1,3,2}]],PalindromeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 22 2018 *)
  • Python
    def a(n): s = str(n); return int(s + s[::-1])
    print([a(n) for n in range(1, 46)]) # Michael S. Branicky, Nov 02 2021

Formula

a(n) = n*10^A055642(n) + A004086(n).
a(n) = 11 * A066492(n).

A240453 Greatest prime divisors of the palindromes with an even number of digits.

Original entry on oeis.org

11, 11, 11, 11, 11, 11, 11, 11, 11, 13, 101, 37, 11, 131, 47, 151, 23, 19, 181, 13, 11, 101, 53, 37, 29, 11, 11, 131, 17, 13, 283, 293, 101, 313, 19, 37, 11, 353, 11, 13, 17, 11, 197, 101, 23, 53, 31, 37, 227, 13, 31, 19, 97, 11, 101, 103, 11, 107, 109, 13
Offset: 1

Views

Author

Michel Lagneau, Apr 05 2014

Keywords

Comments

Greatest prime divisor of A056524(n), or greatest prime divisor of the concatenation of a number n and reverse(n).
The palindromes with an even number of digits are composite numbers divisible by 11. There are many palindromic prime divisors, such as 11, 101, 131, 151, 181, 313, 353, ..., 30103, ...

Examples

			a(10) = 13 because the concatenation of 10 and 01 is 1001 = 7*11*13 where 13 is the greatest divisor of 1001.
		

Crossrefs

Programs

  • Maple
    with(numtheory):for n from 1 to 100 do:x:=convert(n,base,10):n1:=nops(x): s:=sum('x[i]*10^(n1-i)', 'i'=1..n1):y:=n*10^n1+s:z:=factorset(y):n2:=nops(z):d:=z[n2]:printf(`%d, `,d):od:
  • Mathematica
    d[n_]:=IntegerDigits[n];Table[FactorInteger[FromDigits[Join[x=d[n],Reverse[x]]]][[-1,1]],{n,1,100}]
    FactorInteger[#][[-1,1]]&/@Flatten[Table[Select[Range[10^n,10^(n+1)-1],PalindromeQ],{n,1,3,2}]] (* Harvey P. Dale, Dec 06 2021 *)
  • Python
    from sympy import primefactors
    def a(n): s = str(n); return max(primefactors(int(s + s[::-1])))
    print([a(n) for n in range(1, 61)]) # Michael S. Branicky, Nov 11 2021

Formula

a(n) = A006530(A056524(n)).
Showing 1-4 of 4 results.