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 A155030 #8 Jun 14 2019 17:26:44 %S A155030 5,11,17,31,41,67,109,127,157,191,211,241,277,331,367,401,461,509,547, %T A155030 563,587,599,617,739,773,797,859,877,919,967,991,1031,1063,1087,1153, %U A155030 1171,1201,1217,1297,1409,1447,1471,1499,1523,1597,1621,1669,1723,1741 %N A155030 Primes p=A000040(n) with prime index n such that the concatenation n//p is a composite number. %C A155030 Demanding that the index is not a prime would lead to A155025 instead. %e A155030 For the index n=3, a prime, p = prime(3)=5, the concatenation 35 is composite, so p=5 is added to the sequence. %e A155030 For the index n=5, a prime, p = prime(5)=11, the concatenation 511 is composite, so p=11 is added to the sequence. %e A155030 For the index n=6, not a prime, nothing is added to the sequence. %e A155030 For the index n=7, a prime, p = prime(7)=17, the concatenation 717 is composite, so p=17 is added to the sequence. %t A155030 Prime[#]&/@Select[Prime[Range[70]],CompositeQ[FromDigits[Join[ IntegerDigits[ #], IntegerDigits[ Prime[#]]]]]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 14 2019 *) %Y A155030 Cf. A000027, A000040, A002808, A155025. %K A155030 nonn,base %O A155030 1,1 %A A155030 _Juri-Stepan Gerasimov_, Jan 19 2009 %E A155030 Definition clarified, sequence extended by _R. J. Mathar_, Oct 14 2009