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

0, 1, 21, 148, 1078, 7898, 60843, 486390, 3969956, 33123937, 280486145, 2411806083

Offset

1,3

Comments

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).

Links

Table of n, a(n) for n=1..12.

Example

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.

Mathematica

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 *)

Prog

(PARI)
{
\\Variables: E changes with every other\\
\\change in n as bounding smaller prime\\
\\p, b and B are the bounding powers of\\
\\10, e represents the power of 10 just\\
\\above p, q is the larger prime, and c is\\
\\the count of those pq satisfying the\\
\\criterion.\\
print(0); n=2; E=10; b=10; B==100;
while(1,
  p=2; e=10; c=0; while(p<E,
    q=max(nextprime(p+1), nextprime(b/p));
    while(q<B/e,
      if(isprime(p*B/e+q), c++);
      q=nextprime(q+1));
    p=nextprime(p+1); if(p>e, e*=10));
  print(c); n++; b*=10; B*=10; if(n%2==0, E*=10))
}

Crossrefs

Cf. A220296.

Sequence in context: A267992 A060493 A198183 * A253459 A041850 A239123

Adjacent sequences: A259490 A259491 A259492 * A259494 A259495 A259496

Keyword

nonn,base

Author

James G. Merickel, Jun 28 2015

Extensions

a(12) from Giovanni Resta, Jul 13 2015

Status

approved