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Smallest prime followed by n or more composites.
4

%I #15 May 31 2014 19:13:01

%S 2,3,7,7,23,23,89,89,113,113,113,113,113,113,523,523,523,523,887,887,

%T 1129,1129,1327,1327,1327,1327,1327,1327,1327,1327,1327,1327,1327,

%U 1327,9551,9551,15683,15683,15683,15683,15683,15683,15683,15683,19609

%N Smallest prime followed by n or more composites.

%C Except for a(1), records occur at even values of n, and each term appears an even number of times consecutively. (Proof. A maximal run of composites must begin and end at even numbers.) - _Jonathan Sondow_, May 31 2014

%H Charles R Greathouse IV, <a href="/A104138/b104138.txt">Table of n, a(n) for n = 0..1000</a>

%F Record prime A002386(n+1) appears A053695(n-1) times, for n>1.

%F a(n) = A030296(n) - 1, for n > 0. - _Jonathan Sondow_, May 31 2014

%e a(10)=113 because it is the first prime occurring before primes 199,211,293,317,467,509,... all followed by at least ten successive composites.

%Y Cf. A002386, A005250, A030296, A053695.

%K nonn

%O 0,1

%A _Lekraj Beedassy_, Mar 07 2005

%E a(34) corrected by _Charles R Greathouse IV_, Aug 09 2011