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A082563 a(1) = 3; for n>=1, a(n+1) is the smallest palindromic prime with a(n) as a central substring.

%I A082563 #18 Sep 24 2015 01:24:22
%S A082563 3,131,11311,121131121,1212113112121,36121211311212163,
%T A082563 303612121131121216303,7230361212113112121630327,
%U A082563 30723036121211311212163032703,723072303612121131121216303270327,1472307230361212113112121630327032741,114723072303612121131121216303270327411
%N A082563 a(1) = 3; for n>=1, a(n+1) is the smallest palindromic prime with a(n) as a central substring.
%C A082563 The minimal nested palindromic primes with seed 3; see A261881 for a guide to related sequences.
%H A082563 Clark Kimberling, <a href="/A082563/b082563.txt">Table of n, a(n) for n = 1..200</a>
%e A082563 As a triangle:
%e A082563 ........3
%e A082563 .......131
%e A082563 ......11311
%e A082563 ....121131121
%e A082563 ..1212113112121
%e A082563 36121211311212163
%t A082563 s = {3}; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {15}]; s
%t A082563 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A082563 Cf. A053600, A075597, A261881.
%K A082563 nonn,base
%O A082563 1,1
%A A082563 _Benoit Cloitre_, May 04 2003
%E A082563 Name changed by _Arkadiusz Wesolowski_, Sep 15 2011
%E A082563 More terms from _Clark Kimberling_, Sep 23 2015