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a(n) = smallest prime p for which cyclic digit shifts produce exactly n different primes, or 0 if no such p exists for n.
3

%I #35 Aug 11 2024 14:41:34

%S 2,13,113,1193,11939,193939,17773937,119139133,111133719913,

%T 111119917373,111393733793,1117739771979737

%N a(n) = smallest prime p for which cyclic digit shifts produce exactly n different primes, or 0 if no such p exists for n.

%C a(n) is equal to the smallest n-digit non-repunit prime in A016114, unless no n-digit non-repunit prime exists in A016114. In that case, the number of digits of a(n), if it exists, must be > n.

%C From _David A. Corneth_, Aug 06 2018: (Start)

%C Do we have leading digit of a(n) <= any digit from a(n)?

%C For n > 1, can a(n) contain a digit d with gcd(10, d) > 1? (End)

%C Smallest prime p such that A262988(p) = n. - _Felix Fröhlich_, Aug 06 2018

%H P. De Geest, <a href="https://www.worldofnumbers.com/circular.htm">Circular primes</a>

%Y Cf. A016114, A262988. This is column 1 of A317716.

%K nonn,base,more

%O 1,1

%A _Felix Fröhlich_, Nov 21 2014

%E a(7)-a(8) from P. De Geest's website added by _Felix Fröhlich_, Nov 26 2014

%E a(9)-a(12) from _Robert G. Wilson v_, Aug 06 2018