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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.
4
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
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
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