A077379 Smallest n-digit squarefree number whose internal as well as external digits form a squarefree number greater than 1; or 0 if no such number exists.

0, 0, 123, 1021, 10021, 100021, 1000021, 10000021, 100000021, 1000000021, 10000000021, 100000000021, 1000000000021, 10000000000021, 100000000000021, 1000000000000021, 10000000000000021, 100000000000000021, 1000000000000000021, 10000000000000000021, 100000000000000000021, 1000000000000000000021

Offset: 1

Author

Amarnath Murthy, Nov 06 2002

Keywords

• base
• nonn

Comments

Note that the pattern 10^(n-1)+21 is broken for any n == 3 (mod 22), where 10^(n-1)+21 is divisible by 11^2. - Franklin T. Adams-Watters, Jun 13 2006

Examples

			a(5) = 10021 = 11 * 911 is squarefree, internal digits 002 squarefree, external digits 11 squarefree.
a(6) = 100021 = 29 * 3449 has exactly those same properties.
a(7) = 1000021 = 11 * 90911 has exactly those same properties.
a(8) = 10000021 = 97 * 103093 has exactly those same properties.
a(9) = 100000021 = 11 * 19 * 23 * 71 * 293 is similar, though not semiprime.
		

Crossrefs

Cf. A077376, A077377, A077378, A077380.

Extensions

a(5)-a(12) from Jonathan Vos Post, Mar 22 2006

More terms from Franklin T. Adams-Watters, Jun 13 2006