A276803 - OEIS

%I #13 Aug 03 2022 18:59:43

%S 6,21,22,33,39,46,51,58,82,93,111,115,133,141,142,159,166,177,187,201,

%T 205,219,226,235,237,247,249,253,262,267,274,291,301,319,327,355,358,

%U 391,411,427,478,489,501,502,505,511,535,538,543,562,565,573,583,586,589

%N Semiprimes k such that the concatenation of its prime factors is prime.

%C Alternatively: Semiprimes p*q, with p<q, such that the concatenation p || q is a prime.

%C Corresponding primes are at A105184.

%H Charles R Greathouse IV, <a href="/A276803/b276803.txt">Table of n, a(n) for n = 1..10000</a>

%e 21 is a term because 21 = 3 * 7 that is a semiprime : concatenation of 3 and 7 = 37  which is prime.

%e 142 is a term because 142 = 2 * 71 that is a semiprime : concatenation of 2 and 71 = 271 which is prime.

%t Select[Select[Range[1000], PrimeOmega[#] == 2 &], PrimeQ[FromDigits[Join[IntegerDigits [First@First[FactorInteger[#]]], IntegerDigits[First@Last[FactorInteger[#]]]]]] &]

%t Select[Range[1000],PrimeOmega[#]==PrimeNu[#]==2&&PrimeQ[FromDigits[ Flatten[ IntegerDigits/@FactorInteger[#][[All,1]]]]]&] (* _Harvey P. Dale_, Aug 03 2022 *)

%o (PARI) list(lim)=my(v=List()); forprime(p=2,lim\2, forprime(q=2, min(p,lim\p), if(isprime(eval(Str(q,p))), listput(v,p*q)))); Set(v) \\ _Charles R Greathouse IV_, Sep 17 2016

%Y Cf. A000040, A001358, A100607, A105184.

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, Sep 17 2016