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Smallest prime of the form: all fives followed by prime(n). a(n) >prime(n). 0 if no such prime exists.
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%I #20 Dec 05 2013 19:57:14

%S 0,53,0,557,55511,

%T 55555555555555555555555555555555555555555555555555555555555555555555513,

%U 55555517,5519,523,55529,5531,0,541,55555543,547,55555553,55555559

%N Smallest prime of the form: all fives followed by prime(n). a(n) >prime(n). 0 if no such prime exists.

%C Prime(n) is all zeros followed by prime(n). This is all fives followed by prime(n).

%C The next sequence in this progression, "Smallest prime of the form: all sixes followed by prime(n), a(n)> prime(n)", begins 0, 0, 0, 67, then (5) = 2*(10^5039 - 1)/3 - 55, a number that consists of 5037 sixes followed by 2 ones. This does not fit into the constraints of the OEIS. _N. J. A. Sloane_, Nov 20 2005, based on information from Hans Havermann.

%C The large number is quickly certified prime by PARI's APRCL test: isprime(555...513,2) -> 1. - _Hagen von Eitzen_, Jun 17 2009

%C Next term is 5*(10^184 - 1)/9 + 6, containing 184 digits, and is too large to include here. - _Arkadiusz Wesolowski_, Jun 03 2013

%e a(5) = 55511, as 511, 5511 are composite, prime(5) = 11.

%e All positive numbers of the form 5*(10^k - 1)/9 - 18 have a factor in the covering set {3, 7, 13, 37}, so a(12) = 0. - _Arkadiusz Wesolowski_, Jun 03 2013

%Y Cf. A114783, A114784, A114785, A114786.

%K base,nonn

%O 1,2

%A _Amarnath Murthy_, Nov 17 2005

%E More terms from _Joshua Zucker_, May 06 2006

%E Edited by _T. D. Noe_, Oct 30 2008

%E a(12)-a(17) from _Arkadiusz Wesolowski_, Jun 03 2013