A181739 Smallest semiprime with internal digits = n; or 0 if no such number exists.

106, 111, 121, 133, 141, 155, 161, 177, 183, 194, 1101, 1111, 1121, 1133, 1141, 1154, 1165, 1174, 1186, 1191, 1202, 1211, 1226, 1234, 1241, 1253, 1261, 1271, 1282, 1293, 1306, 1313, 1322, 1333, 1343, 1351, 1363, 1371, 1382, 1391, 1401, 1411, 2426

Offset: 0

Author

Jonathan Vos Post, Jan 31 2011

Keywords

• nonn
• base

Comments

This is to A069691 as semiprimes A001358 are to primes A000040.

By placing one digit on both sides of n (1..9 on the left and on the right) one gets 81 different numbers that might be semiprimes. If none of these numbers is a semiprime then a(n) = 0.

The smallest n such that a(n) = 0 is 20056492. - Donovan Johnson, Feb 01 2011

If one or more digits are allowed on both sides of n, the smallest semiprime containing 20056492 is 10200564926 = 2*5100282463.

Examples

			a(23) = 1234 = 2 * 617 has the embedded substring 1"23"4.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001358, A032734, A069691.

Programs

Maple

a:= proc(n) local i, j, k;
      for i to 9 do
        for j to 9 do
          k:= parse(cat(i, n, j));
          if not isprime(k) and add(t[2], t=ifactors(k)[2])=2
             then return k fi
        od
      od; return 0;
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Feb 01 2011

Extensions

More terms from Alois P. Heinz, Feb 01 2011