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