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A087911 Smallest prime p that is a palindrome in n different bases < p. 3

%I #28 Jul 02 2017 04:27:45

%S 2,3,5,17,191,257,1009,4561,4591,21601,57601,54121,86677,176401,

%T 415801,291721,950041,1259701,3049201,1670761,6098401,3880801,5654881,

%U 13759201,18618601,14414401,18960481,15135121,31600801,45405361,35814241

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

%C a(n) = A000040(A137779^(-1)(n)). - Attila Olah (jolafix(AT)gmail.com), May 06 2008, corrected May 08 2008

%C The sequence is not monotonic: a(10) > a(11) = 54121. - Attila Olah (jolafix(AT)gmail.com), May 06 2008, corrected May 08 2008

%H Karl Hovekamp, Jan 01 2007, <a href="/A087911/b087911.txt">Table of n, a(n) for n = 1..55</a>

%H K. Hovekamp, <a href="http://free.pages.at/neuenkirchen/palindrom/">Palindromic numbers</a> [Broken link?]

%e 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 a(12) = 54121 because 54121 is a palindrome in 12 different bases, including base 1 and base 54120.

%o (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 Cf. A137779, A037183, A107129, A065531, A135549.

%K base,nonn

%O 1,1

%A _Randy L. Ekl_, Oct 17 2003

%E More terms from _David Wasserman_, Jun 20 2005

%E Terms a(17)-a(22) computed by _Karl Hovekamp_, sent by _David Wasserman_, Dec 19 2006

%E More terms from _Karl Hovekamp_, Jan 01 2007

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)