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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

Table of n, a(n) for n=1..68.

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

Cf. A060873-A060879, A060947-A060949, A123586.

Sequence in context: A037084 A018935 A039501 * A138579 A189703 A158251

Adjacent sequences:  A114252 A114253 A114254 * A114256 A114257 A114258

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

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Last modified February 25 12:00 EST 2021. Contains 341606 sequences. (Running on oeis4.)