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%I #12 Jun 13 2014 19:13:23
%S 19,139,3089,18839,123229,2134519,12130109,23884639,363289219,
%T 9568590299,24037796539,130426565719,405033487139,3553144754209,
%U 4010803176619,71894236537009,71894236537009
%N Initial prime in first sequence of n primes congruent to 4 modulo 5. The first prime in a sequence of length n all ending with the digit 9.
%H J. K. Andersen, <a href="http://primerecords.dk/congruent-primes.htm">Consecutive Congruent Primes</a>.
%e a(5) = 123229 because this number is the first in a sequence of 5 consecutive primes all of the form 5n + 4.
%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 ] != {4}, 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 Cf. A054681, A057618, A057631, A068150.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Oct 10 2000
%E Phil Carmody gives a(15)= 4010803176619 in A054681
%E More terms from _Jens Kruse Andersen_, Jun 03 2006
%E a(16)-a(17) from _Giovanni Resta_, Aug 01 2013