A238331 The prime(n)-th prime number ending in prime(n), or 0 if none exists.

0, 23, 0, 107, 2411, 3413, 5417, 4919, 5923, 8629, 9931, 10937, 14741, 14243, 16747, 18553, 19259, 22961, 24767, 28571, 24373, 31079, 29483, 33589, 35597, 498101, 475103, 528107, 555109, 570113, 607127, 641131, 659137, 717139, 756149, 786151, 754157, 817163

Offset: 1

Author

T. D. Noe, Feb 27 2014

Keywords

• nonn
• base

Comments

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.

Examples

			23 is the third prime ending with 3.
107 is the seventh prime ending in 7.
2411 is the 11th prime ending in 11.
3413 is the 13th prime ending in 13 -- a very unlucky prime.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A000040 (prime numbers).

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

Programs

Mathematica

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