cp's OEIS Frontend

A087911 Smallest prime p that is a palindrome in n different bases < p.

%I A087911 #28 Jul 02 2017 04:27:45
%S A087911 2,3,5,17,191,257,1009,4561,4591,21601,57601,54121,86677,176401,
%T A087911 415801,291721,950041,1259701,3049201,1670761,6098401,3880801,5654881,
%U A087911 13759201,18618601,14414401,18960481,15135121,31600801,45405361,35814241
%N A087911 Smallest prime p that is a palindrome in n different bases < p.
%C A087911 a(n) = A000040(A137779^(-1)(n)). - Attila Olah (jolafix(AT)gmail.com), May 06 2008, corrected May 08 2008
%C A087911 The sequence is not monotonic: a(10) > a(11) = 54121. - Attila Olah (jolafix(AT)gmail.com), May 06 2008, corrected May 08 2008
%H A087911 Karl Hovekamp, Jan 01 2007, <a href="/A087911/b087911.txt">Table of n, a(n) for n = 1..55</a>
%H A087911 K. Hovekamp, <a href="http://free.pages.at/neuenkirchen/palindrom/">Palindromic numbers</a> [Broken link?]
%e A087911 a(4) = 191 because 191 base 6 = 515, 191 base 9 = 232, 191 base 10 = 191 and 191 base 190 = 11, all palindromes. No numbers less than 191 can be represented in 4 such ways.
%e A087911 a(12) = 54121 because 54121 is a palindrome in 12 different bases, including base 1 and base 54120.
%o A087911 (PARI) q=1; forprime(m=3,20000,count=0; for(b=2,m-1, w=b+1; k=0; i=m; while(i>0,k=k*w+i%b; i=floor(i/b)); l=0; j=k; while(j>0,l=l*w+j%w; j=floor(j/w)); if(l==k,count=count+1,); if(count>q,print1(m,", "); q=count,)))
%Y A087911 Cf. A137779, A037183, A107129, A065531, A135549.
%K A087911 base,nonn
%O A087911 1,1
%A A087911 _Randy L. Ekl_, Oct 17 2003
%E A087911 More terms from _David Wasserman_, Jun 20 2005
%E A087911 Terms a(17)-a(22) computed by _Karl Hovekamp_, sent by _David Wasserman_, Dec 19 2006
%E A087911 More terms from _Karl Hovekamp_, Jan 01 2007