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%I #9 Jun 13 2014 19:18:41
%S 19,523,15823,655453,19256491,24084793,303392377,3408167431,
%T 17875882441,179445819277,1563518842687
%N Initial prime in first sequence of n primes congruent to 1 modulo 9.
%H J. K. Andersen, <a href="http://primerecords.dk/congruent-primes.htm">Consecutive Congruent Primes</a>.
%e a(3) = 15823 because this number is the first in a sequence of 3 consecutive primes all of the form 9n + 1.
%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 ] != {1}, k = NextPrime[ k ]; a = Take[ AppendTo[ a, Mod[ k, 9 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 7} ] a(8) > 1655036000.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Oct 11 2000
%E More terms from _Jens Kruse Andersen_, May 31 2006
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