# Happy New Palindromic Year 11111011111 !

Posted 7 years ago
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 Very nice palindromic binary year for everybody! IntegerDigits[2015, 2] {1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1}
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Posted 7 years ago
 I noticed another interesting coincidence (?) about "2015": which are: 2015 (base 11) converted to base 10 is 2678. 2015 (base 10) converted to base 9 is 2678. Well, these have actually been in alignment since the year 2010, when both computations yielded 2673, but did anyone notice before?
Posted 7 years ago
 Palindromes in base 2 are rare but for a number to be a palindrome in some base is not so rare. For instance there are a few other bases that make 2015 into a palindrome: Select[Range[2, 2013], # == Reverse[#] &[IntegerDigits[2015, #]] &] {2, 38, 64, 154, 402}For {1,1} is always b+1 palindrome, so any nontrivial palindrome base is between 2 and n-2. It is rare to not be a palindrome in any such base. The last one was 2011 and the next one is 2063. Select[Range[1900, 2200], Function[n, Select[Range[2, n - 2], # == Reverse[#] &[IntegerDigits[n, #]] &] === {}]] {1907, 1949, 1993, 1997, 2011, 2063, 2087, 2099, 2111, 2137, 2179}
 It is also a Lucas-Carmichel number. n = 2015; factors = FactorInteger[n][[All, 1]]; AllTrue[factors + 1, Divisible[n + 1, #] &] TrueSee this link: LucasCarmichael number-adk-