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

2, 3, 5, 17, 191, 257, 1009, 4561, 4591, 21601, 57601, 54121, 86677, 176401, 415801, 291721, 950041, 1259701, 3049201, 1670761, 6098401, 3880801, 5654881, 13759201, 18618601, 14414401, 18960481, 15135121, 31600801, 45405361, 35814241

Offset: 1

Author

Randy L. Ekl, Oct 17 2003

Keywords

• base
• nonn

Comments

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

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

Examples

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

Links

• Karl Hovekamp, Jan 01 2007, Table of n, a(n) for n = 1..55
• K. Hovekamp, Palindromic numbers [Broken link?]

Crossrefs

Cf. A137779, A037183, A107129, A065531, A135549.

Programs

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,)))

Extensions

More terms from David Wasserman, Jun 20 2005

Terms a(17)-a(22) computed by Karl Hovekamp, sent by David Wasserman, Dec 19 2006

More terms from Karl Hovekamp, Jan 01 2007