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A249974 a(1)=1; otherwise, find the first digit from the left in a(n-1) which is 1, 3, 7 or 9. Omitting the digits before this one, we reverse the remaining digits, obtaining s, say. Then a(n) is the smallest prime which ends with s and has not already appeared.

%I A249974 #47 Nov 07 2023 03:16:42
%S A249974 1,11,211,311,2113,2311,5113,6311,6113,8311,11113,131111,3111131,
%T A249974 21311113,63111131,31311113,31111313,531311113,1131111313,
%U A249974 273131111311,311311113137,5731311113113,6311311113137,12731311113113,2331131111313721
%N A249974 a(1)=1; otherwise, find the first digit from the left in a(n-1) which is 1, 3, 7 or 9. Omitting the digits before this one, we reverse the remaining digits, obtaining s, say. Then a(n) is the smallest prime which ends with s and has not already appeared.
%C A249974 The sequence is infinite. Indeed, by [Sierpiński] (see also Theorem 21 in [Trost]) for given decimal digits c_1..c_m such that c_m equals 1,3,7 or 9, there are infinitely many primes ending with c_1..c_m.
%D A249974 W. Sierpiński, Sur l'existence de nombres premiers avec une suite arbitraire de chiffres initiaux, Le Matematiche Catania, 1951.
%D A249974 E. Trost, Primzahlen, Verlag Birkhäuser, 1953, Theorems 20 - 21.
%e A249974 Let n=6. Since a(5)=2113, then, omitting 2, we obtain the number 113 whose reverse is s=311. The smallest prime ending with 311 is 2311. So a(6)=2311.
%Y A249974 Cf. A000040, A262373.
%K A249974 nonn,base
%O A249974 1,2
%A A249974 _Vladimir Shevelev_, Sep 20 2015