This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A155025 #10 Jul 16 2015 21:49:48
%S A155025 2,19,23,29,43,47,53,71,73,79,89,97,101,107,131,137,139,163,167,173,
%T A155025 193,223,227,229,233,239,257,281,293,307,311,313,317,337,347,349,359,
%U A155025 373,379,383,389,397,409,419,433,443,449,457,463,467,491,499,503,521,541,557,569
%N A155025 Primes p=A000040(n) with nonprime index n such that the concatenation n//p is a composite number.
%H A155025 Harvey P. Dale, <a href="/A155025/b155025.txt">Table of n, a(n) for n = 1..10000</a>
%e A155025 For the nonprime n=1, p = prime(n) = 2, the concatenation is 12 is composite, and p is added to the sequence.
%e A155025 For the nonprime n=8, p = prime(8) = 19, the concatenation 819 is composite, and p=19 is added to the sequence.
%e A155025 For the nonprime n=12, p = prime(12) = 37, the concatenation 1237 is prime, so p=37 is not added to the sequence.
%t A155025 cnQ[{n_,p_}]:=!PrimeQ[n]&&!PrimeQ[FromDigits[Flatten[ IntegerDigits/@ {n,p}]]]; Transpose[Select[Table[{n,Prime[n]},{n,150}],cnQ]][[2]] (* _Harvey P. Dale_, Dec 18 2012 *)
%Y A155025 Cf. A000040, A003808, A141468, A155030.
%K A155025 nonn,base
%O A155025 1,1
%A A155025 _Juri-Stepan Gerasimov_, Jan 19 2009
%E A155025 Definition clarified, sequence extended by _R. J. Mathar_, Oct 14 2009