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

1,3

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

Links

Table of n, a(n) for n=1..22.

Example

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.

Sequence in context: A181679 A193251 A074303 * A135475 A233119 A167231

Adjacent sequences: A077376 A077377 A077378 * A077380 A077381 A077382

Keyword

base,nonn

Author

Amarnath Murthy, Nov 06 2002

Extensions

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

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

Status

approved