A110408 Smallest prime which is the repeated reverse concatenation of n followed by n (ending in n), where n == 1,3,7 or 9 (mod 10), or 0 if no such prime exists.

11, 0, 0, 0, 0, 3131313131313131313113, 71717117, 9191919191919119, 0, 32323223, 0, 9292929292929292929229, 13131331, 0, 7373737373737373737373737373737373737373737337, 0, 14141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141441

Offset: 0

Author

Amarnath Murthy, Jul 30 2005

Keywords

• base
• easy
• nonn

Comments

Conjecture: a(n) is 0 iff n is a palindromic prime == 1,3,7 or 9 (mod 10) and/or n ==0 (mod 3). As rev(n) followed by n is == 0 (mod 11), hence every nonzero term contains at least two reverse concatenations of n followed by n.

The larger numbers are probable primes. - Joshua Zucker, May 10 2006

The Magma Calculator (http://magma.maths.usyd.edu.au/calc/) verified each of the nine nonzero terms as prime. - Jon E. Schoenfield, Aug 24 2009

Crossrefs

Cf. A110409.

Extensions

More terms from Joshua Zucker, May 10 2006

Edited by T. D. Noe, Oct 30 2008