A155030 Primes p=A000040(n) with prime index n such that the concatenation n//p is a composite number.
5, 11, 17, 31, 41, 67, 109, 127, 157, 191, 211, 241, 277, 331, 367, 401, 461, 509, 547, 563, 587, 599, 617, 739, 773, 797, 859, 877, 919, 967, 991, 1031, 1063, 1087, 1153, 1171, 1201, 1217, 1297, 1409, 1447, 1471, 1499, 1523, 1597, 1621, 1669, 1723, 1741
Offset: 1
Examples
For the index n=3, a prime, p = prime(3)=5, the concatenation 35 is composite, so p=5 is added to the sequence. For the index n=5, a prime, p = prime(5)=11, the concatenation 511 is composite, so p=11 is added to the sequence. For the index n=6, not a prime, nothing is added to the sequence. For the index n=7, a prime, p = prime(7)=17, the concatenation 717 is composite, so p=17 is added to the sequence.
Programs
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Mathematica
Prime[#]&/@Select[Prime[Range[70]],CompositeQ[FromDigits[Join[ IntegerDigits[ #], IntegerDigits[ Prime[#]]]]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 14 2019 *)
Extensions
Definition clarified, sequence extended by R. J. Mathar, Oct 14 2009
Comments