%I #15 Jul 14 2016 17:09:01
%S 5,389,2213,45013,73133,1319861,3250469,29662253,35677501,101341613,
%T 12664911341,12664911341,124809839701,132932904029,1181960064853,
%U 20151469541389,20151469541389,20151469541389,102573904861013
%N Initial prime in first sequence of n primes congruent to 5 modulo 8.
%H J. K. Andersen, <a href="http://primerecords.dk/congruent-primes.htm">Consecutive Congruent Primes</a>.
%e a(3) = 2213 because this number is the first in a sequence of 3 consecutive primes all of the form 8n + 5.
%t NextPrime[ n_Integer ] := Module[ {k = n + 1}, While[ ! PrimeQ[ k ], k++ ]; Return[ k ] ]; PrevPrime[ n_Integer ] := Module[ {k = n - 1}, While[ ! PrimeQ[ k ], k-- ]; Return[ k ] ]; p = 0; Do[ a = Table[ -1, {n} ]; k = Max[ 1, p ]; While[ Union[ a ] != {5}, k = NextPrime[ k ]; a = Take[ AppendTo[ a, Mod[ k, 8 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[[ -2 ] ] ]; p = p[[ -1 ] ], {n, 1, 9} ]
%t Prime[#[[1,1]]]&/@Table[SequencePosition[Table[If[Mod[Prime[n],8]==5,1,0],{n,6*10^6}],PadRight[{},i,1],1],{i,10}] (* The program uses the SequencePosition function from Mathematica version 10. It generates only the first ten terms. It could be modified to generate more but it would take increasingly lengthy times to generate the higher terms. *)
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Oct 10 2000
%E More terms from _Jens Kruse Andersen_, May 28 2006
%E a(16)-a(19) from _Giovanni Resta_, Aug 04 2013
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