cp's OEIS Frontend

A259493 Number of n-digit semiprimes whose prime factors concatenated larger to the right of smaller form an n-digit prime (in decimal).

%I A259493 #34 Jul 13 2015 11:19:03
%S A259493 0,1,21,148,1078,7898,60843,486390,3969956,33123937,280486145,
%T A259493 2411806083
%N A259493 Number of n-digit semiprimes whose prime factors concatenated larger to the right of smaller form an n-digit prime (in decimal).
%C A259493 For n>2, A220296(n)>a(n), with the numbers counted to obtain A220296(n) being a proper superset of the numbers counted for a(n) (and the example here being unique for both for n<3).
%e A259493 21=3*7 produces the prime 37 via the described concatenation, and it is the only 2-digit semiprime that does produce a 2-digit prime like this, making a(2)=1.
%t A259493 f[n_] := Block[{g, s}, s = Select[Range[10^(n - 1), 10^n - 1], PrimeOmega@ # == 2 &]; g[x_] := FromDigits[IntegerDigits[First /@ FactorInteger[x]] // Flatten]; Select[s, And[IntegerLength[g@ #] == n, PrimeQ@ g@ #] &]]; Length@ f@ # & /@ Range@ 6 (* _Michael De Vlieger_, Jul 01 2015 *)
%o A259493 (PARI)
%o A259493 {
%o A259493 \\Variables: E changes with every other\\
%o A259493 \\change in n as bounding smaller prime\\
%o A259493 \\p, b and B are the bounding powers of\\
%o A259493 \\10, e represents the power of 10 just\\
%o A259493 \\above p, q is the larger prime, and c is\\
%o A259493 \\the count of those pq satisfying the\\
%o A259493 \\criterion.\\
%o A259493 print(0);n=2;E=10;b=10;B==100;
%o A259493 while(1,
%o A259493   p=2;e=10;c=0;while(p<E,
%o A259493     q=max(nextprime(p+1),nextprime(b/p));
%o A259493     while(q<B/e,
%o A259493       if(isprime(p*B/e+q),c++);
%o A259493       q=nextprime(q+1));
%o A259493     p=nextprime(p+1);if(p>e,e*=10));
%o A259493   print(c);n++;b*=10;B*=10;if(n%2==0,E*=10))
%o A259493 }
%Y A259493 Cf. A220296.
%K A259493 nonn,base
%O A259493 1,3
%A A259493 _James G. Merickel_, Jun 28 2015
%E A259493 a(12) from _Giovanni Resta_, Jul 13 2015