%I #13 Sep 08 2022 08:45:40

%S 4,6,12,18,27,30,35,36,42,45,46,54,56,57,58,82,85,92,93,99,115,117,

%T 119,121,123,136,141,145,147,159,161,171,175,176,177,206,215,222,225,

%U 237,243,261,273,274,282,285,291,295,296,303,309,315,319,322,327,328,332

%N Composites n such that concatenation of n and n-th prime is prime.

%H Vincenzo Librandi, <a href="/A154965/b154965.txt">Table of n, a(n) for n = 1..1000</a>

%e Concatenation of composite 4 and fourth prime 7 is the prime 47, hence 4 is in the sequence. Concatenation of composite 36 and 36th prime 151 is the prime 36151, hence 36 is in the sequence.

%t concatQ[n_]:=PrimeQ[FromDigits[Join[IntegerDigits[n],IntegerDigits[ Prime[n]]]]]; nn=400;Select[Complement[Range[nn],Prime[Range[ PrimePi[nn]]]],concatQ] (* _Harvey P. Dale_, Jun 05 2011 *)

%o (Magma) [ n: n in [1..340] | not IsPrime(n) and IsPrime(StringToInteger(IntegerToString(n) cat IntegerToString(NthPrime(n)))) ];

%Y Cf. A000040 (primes), A002808 (composites).

%K nonn,base,easy,less

%O 1,1

%A _Juri-Stepan Gerasimov_, Jan 18 2009

%E Edited and extended beyond a(4) by _Klaus Brockhaus_, Jan 20 2009