A259493 - OEIS

%I #34 Jul 13 2015 11:19:03

%S 0,1,21,148,1078,7898,60843,486390,3969956,33123937,280486145,

%T 2411806083

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

%C 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 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 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 (PARI)

%o {

%o \\Variables: E changes with every other\\

%o \\change in n as bounding smaller prime\\

%o \\p, b and B are the bounding powers of\\

%o \\10, e represents the power of 10 just\\

%o \\above p, q is the larger prime, and c is\\

%o \\the count of those pq satisfying the\\

%o \\criterion.\\

%o print(0);n=2;E=10;b=10;B==100;

%o while(1,

%o   p=2;e=10;c=0;while(p<E,

%o     q=max(nextprime(p+1),nextprime(b/p));

%o     while(q<B/e,

%o       if(isprime(p*B/e+q),c++);

%o       q=nextprime(q+1));

%o     p=nextprime(p+1);if(p>e,e*=10));

%o   print(c);n++;b*=10;B*=10;if(n%2==0,E*=10))

%o }

%Y Cf. A220296.

%K nonn,base

%O 1,3

%A _James G. Merickel_, Jun 28 2015

%E a(12) from _Giovanni Resta_, Jul 13 2015