%I A016038
%S A016038 0,1,2,3,4,6,11,19,47,53,79,103,137,139,149,163,167,179,223,263,269,283,
               293,
%T A016038 311,317,347,359,367,389,439,491,563,569,593,607,659,739,827,853,877,
%U A016038 977,983,997,1019,1049,1061,1187,1213,1237,1367,1433,1439,1447,1459
%N A016038 Strictly nonpalindromic numbers: n is not palindromic in any base b with 
               2 <= b <= n-2.
%C A016038 All elements of the sequence greater than 6 are prime (ab=a(b-1)+a or 
               a^2=(a-1)^2+2(a-1)+1). Mersenne and Fermat primes are not in the 
               sequence.
%C A016038 Additional comments: if you can factor a number as a*b then it is a palindrome 
               in base b-1, where b is the larger of the two factors. (If the number 
               is a square, then it can be a palindrome in an additional way, in 
               base (sqrt(n)-1)). The ab form does not work when a = b-1, but of 
               course there are no two consecutive primes (other than 2,3, which 
               explains the early special cases), so if you can factor a number 
               as a(a-1), then another factorization also exists). - Michael B Greenwald 
               (mbgreen(AT)central.cis.upenn.edu), Jan 01, 2002
%C A016038 Note that no prime p is palindromic in base b for the range sqrt(p) < 
               b < p-1. Hence to find nonpalindromic primes, we need only examine 
               bases up to floor(sqrt(p)), which greatly reduces the computational 
               effort required. - T. D. Noe, Mar 01 2008
%D A016038 Paul Guinand, Strictly non-palindromic numbers, unpublished note, 1996.
%H A016038 T. D. Noe, <a href="b016038.txt">Table of n, a(n) for n=1..10001</a>
%H A016038 K. S. Brown, <a href="http://www.mathpages.com/home/kmath359.htm">On 
               General Palindromic Numbers</a>
%H A016038 P. De Geest, <a href="http://www.worldofnumbers.com/nobase10.htm">Palindromic 
               numbers beyond base 10</a>
%H A016038 John P. Linderman, <a href="a135549.html">Description of A135549-A016038</
               a>
%H A016038 John P. Linderman, <a href="a135549.txt">Perl program</a> [Use the command: 
               HASNOPALINS=1 palin.pl]
%t A016038 PalindromicQ[n_, base_] := FromDigits[Reverse[IntegerDigits[n, base]], 
               base] == n; PalindromicBases[n_] := Select[Range[2, n-2], PalindromicQ[n, 
               # ] &]; StrictlyPalindromicQ[n_] := PalindromicBases[n] == {}; Select[Range[150], 
               StrictlyPalindromicQ] - Herman Beeksma (herman(AT)beeksma.nl), Jul 
               16 2005
%t A016038 palindromicBases[n_] := Module[{p}, Table[p = IntegerDigits[n, b]; If[ 
               p == Reverse[p], {b, p}, Sequence @@ {}], {b, 2, n - 2}]]; lst = 
               {0, 1, 4, 6}; Do[ If[ Length@ palindromicBases@ Prime@n == 0, AppendTo[lst, 
               Prime@n]], {n, 10000}]; lst (from Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Mar 08 2008)
%Y A016038 Cf. A047811, A050813, A050812, A135550, A135551, A135549.
%Y A016038 Cf. A037183, A135550, A135551, A135549, A138348.
%Y A016038 Sequence in context: A111124 A117308 A114412 this_sequence A003099 A061941 
               A029505
%Y A016038 Adjacent sequences: A016035 A016036 A016037 this_sequence A016039 A016040 
               A016041
%K A016038 nonn,base,nice
%O A016038 1,3
%A A016038 Robert G. Wilson v (rgwv(AT)rgwv.com)
%E A016038 Extended and corrected by Patrick De Geest (pdg(AT)worldofnumbers.com), 
               Oct 15 1999.
%E A016038 Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 09 2008