%I A057638
%S A057638 17,89,2593,20809,208393,2663897,7336457,42453937,42453937,1506473153,
%T A057638 24771906961,123737745289,152368449001,152368449001,4990160038937
%N A057638 Initial prime in first sequence of n primes congruent to 1 modulo 8.
%H A057638 J. K. Andersen, <a href="http://users.cybercity.dk/~dsl522332/math/congruent-primes.htm">
               Consecutive Congruent Primes</a>.
%e A057638 a(4) = 20809 because this number is the first in a sequence of 4 consecutive 
               primes all of the form 8n + 1.
%t A057638 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, 8 ] ], -n ] ]; p = NestList[ 
               PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 
               9} ] a(10) > 123700000.
%Y A057638 Sequence in context: A139947 A162930 A138338 this_sequence A159676 A061971 
               A061222
%Y A057638 Adjacent sequences: A057635 A057636 A057637 this_sequence A057639 A057640 
               A057641
%K A057638 nonn
%O A057638 1,1
%A A057638 Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 10 2000
%E A057638 More terms from Jens Kruse Andersen (jens.k.a(AT)get2net.dk), May 28 
               2006