%I A057631
%S A057631 3,283,6793,22963,752023,2707163,44923183,44923183,961129823,1147752443,
%T A057631 6879806623,131145172583,177746482483,795537219143,4028596340953,
%U A057631 6987191424553
%N A057631 Initial prime in first sequence of n primes congruent to 3 modulo 5.
%D A057631 Carlos Rivera's The prime puzzles & problems connection, Puzzle 16 - 
               Consecutive primes and ending digit
%H A057631 J. K. Andersen, <a href="http://users.cybercity.dk/~dsl522332/math/congruent-primes.htm">
               Consecutive Congruent Primes</a>.
%e A057631 a(6) = 2707163 because this number is the first in a sequence of 6 consecutive 
               primes all of the form 5n + 3.
%t A057631 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 ] != {3}, k = NextPrime[ 
               k ]; a = Take[ AppendTo[ a, Mod[ k, 5 ] ], -n ] ]; p = NestList[ 
               PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 
               9} ]
%Y A057631 Sequence in context: A057599 A054583 A139984 this_sequence A058455 A116532 
               A124357
%Y A057631 Adjacent sequences: A057628 A057629 A057630 this_sequence A057632 A057633 
               A057634
%K A057631 nonn
%O A057631 1,1
%A A057631 Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 10 2000
%E A057631 a(10) from Jud McCranie, Jan 14 2003
%E A057631 More terms from Jens Kruse Andersen (jens.k.a(AT)get2net.dk), Jun 03 
               2006