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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.
2

%I #14 Jul 06 2019 14:20:27

%S 11,0,0,0,0,3131313131313131313113,71717117,9191919191919119,0,

%T 32323223,0,9292929292929292929229,13131331,0,

%U 7373737373737373737373737373737373737373737337,0,14141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141441

%N 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.

%C 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.

%C The larger numbers are probable primes. - _Joshua Zucker_, May 10 2006

%C 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

%Y Cf. A110409.

%K base,easy,nonn

%O 0,1

%A _Amarnath Murthy_, Jul 30 2005

%E More terms from _Joshua Zucker_, May 10 2006

%E Edited by _T. D. Noe_, Oct 30 2008