login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A114255 Numbers that are nontrivial (3 digits or more) palindromes when expressed in some base 2 or greater. 2
5, 7, 9, 10, 13, 15, 16, 17, 20, 21, 23, 25, 26, 27, 28, 29, 31, 33, 34, 36, 37, 38, 40, 41, 42, 43, 45, 46, 49, 50, 51, 52, 55, 56, 57, 59, 61, 62, 63, 64, 65, 67, 68, 71, 72, 73, 74, 78, 80, 81, 82, 83, 85, 86, 88, 89, 91, 92, 93, 97, 98, 99, 100, 101, 104, 105, 107, 109 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All integers are trivially palindromes in base 1. All integers n>2 are trivially 2-digit palindromes because they can be represented as "11" in base n-1.
LINKS
EXAMPLE
5 is present because the palindrome (101 base 2) = 5; 803 is present because (30203 base 4) = 803.
MATHEMATICA
palindromeQ[n_, b_] := (id = IntegerDigits[n, b]) === Reverse[id] && Length[id] >= 3; palindromeQ[n_] := Or @@ (palindromeQ[n, #] & ) /@ Range[2, n-2]; Select[ Range[110], palindromeQ] (* Jean-François Alcover, Dec 16 2011 *)
PROG
(Haskell) isPalindrome s = (s == reverse s) digits 0 _ = [] digits n b = n `rem` b : digits (n `quot` b) b check n = any isPalindrome $ takeWhile (\x -> length x > 2) $ map (digits n) [2..] main = mapM print $ filter check [1..]
(PARI) isok(n) = for (b=2, n-1, if ((d=digits(n, b)) && (#d >= 3) && (Vecrev(d) == d), return (1)); ); \\ Michel Marcus, Jul 28 2016
CROSSREFS
Sequence in context: A037084 A018935 A039501 * A350496 A358314 A138579
KEYWORD
easy,base,nonn
AUTHOR
Jason Orendorff (jason.orendorff(AT)gmail.com), Feb 05 2006
EXTENSIONS
Cross-references from Charles R Greathouse IV, Aug 04 2010
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 18 22:18 EDT 2024. Contains 371782 sequences. (Running on oeis4.)