A113598 Least n-digit prime whose digit permutations yield at least n distinct primes, or 0 if no such prime exists.

2, 13, 103, 1009, 10007, 100019, 1000033, 10000019, 100000007, 1000000007, 10000000019, 100000000019, 1000000000039, 10000000000037, 100000000000031, 1000000000000037, 10000000000000061, 100000000000000013

Offset

1,1

Comments

Conjecture: No term is zero.

Leading zeros do not add to the digit count of a(n) but to the digit-count of the permutations. In a(5)=10007, the permutations 10007, 00107, 00017, 70001, 07001, 00701 and 00071 are all primes and their number is >=5. - R. J. Mathar, Feb 07 2008

In a variant where leading zeros may enhance the digit count of a(n), the sequence were 2, 13, 13, 13, 17, 17, 17, 17, 17, 17, 17, 17, 113, 113, 113,.... where 13 acts as a 2-digit prime, as the 3-digit prime 013 and as the 4-digit prime 0013, generating 13, 31 and 103. - R. J. Mathar, Feb 07 2008

Links

Table of n, a(n) for n=1..18.

Example

a(4) = 1009: the four primes arising as digit permutations are 9001, 1009, 0019 and 0109.

Crossrefs

Cf. A000040, A046810, A131371.

Sequence in context: A046893 A354159 A126036 * A125589 A007809 A259146

Adjacent sequences: A113595 A113596 A113597 * A113599 A113600 A113601

Keyword

base,easy,nonn

Author

Amarnath Murthy, Nov 07 2005

Extensions

Corrected and extended by R. J. Mathar, Feb 07 2008

Status

approved