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%I #17 Jul 15 2017 11:25:42
%S 3,283,6793,22963,752023,2707163,44923183,44923183,961129823,
%T 1147752443,6879806623,131145172583,177746482483,795537219143,
%U 4028596340953,6987191424553,269013937530553,281659318133953,281659318133953
%N Initial prime in first sequence of n primes congruent to 3 modulo 5.
%H J. K. Andersen, <a href="http://primerecords.dk/congruent-primes.htm">Consecutive Congruent Primes</a>.
%H Carlos Rivera's The prime puzzles & problems connection, <a href="http://www.primepuzzles.net/puzzles/puzz_016.htm">Puzzle 16 - Consecutive primes and ending digit</a>
%e a(6) = 2707163 because this number is the first in a sequence of 6 consecutive primes all of the form 5n + 3.
%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 ] != {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} ]
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Oct 10 2000
%E a(10) from _Jud McCranie_, Jan 14 2003
%E More terms from _Jens Kruse Andersen_, Jun 03 2006
%E a(17)-a(19) from _Giovanni Resta_, Aug 04 2013
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