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The prime(n)-th prime number ending in prime(n), or 0 if none exists.
1

%I #11 Feb 28 2014 13:44:49

%S 0,23,0,107,2411,3413,5417,4919,5923,8629,9931,10937,14741,14243,

%T 16747,18553,19259,22961,24767,28571,24373,31079,29483,33589,35597,

%U 498101,475103,528107,555109,570113,607127,641131,659137,717139,756149,786151,754157,817163

%N The prime(n)-th prime number ending in prime(n), or 0 if none exists.

%C The first number ending in prime(n) is, of course, prime(n). The numbers 2 and 5 are zero because there are no additional primes ending in those numbers; they are the numbers divisible by 2 or 5.

%H T. D. Noe, <a href="/A238331/b238331.txt">Table of n, a(n) for n = 1..200</a>

%e 23 is the third prime ending with 3.

%e 107 is the seventh prime ending in 7.

%e 2411 is the 11th prime ending in 11.

%e 3413 is the 13th prime ending in 13 -- a very unlucky prime.

%t ps = Prime[Range[PrimePi[1000000]]]; t = {}; p = 1; done = False; While[! done,p = NextPrime[p]; len = Length[IntegerDigits[p]]; s = Select[ps, Mod[#, 10^len] == p &, p]; If[Length[s] < p, If[MemberQ[{2, 5}, p], AppendTo[t, 0], done = True], AppendTo[t, s[[-1]]]]]; t

%Y Cf. A000040 (prime numbers).

%Y Cf. A030431, A030432, A167442 (primes ending in 3, 7, 11).

%K nonn,base

%O 1,2

%A _T. D. Noe_, Feb 27 2014