%I #16 May 28 2023 15:40:39

%S 3,491,2243,42299,274123,4310083,4310083,9065867,547580443,1885434347,

%T 8674616939,11312238283,19201563659,619849118491,4056100954547,

%U 13721202685691,119254168189363,276151474703651,2189798979924331,3153425741761723

%N Initial prime in first sequence of n primes congruent to 3 modulo 8.

%H J. K. Andersen, <a href="http://primerecords.dk/congruent-primes.htm">Consecutive Congruent Primes</a>.

%e a(3) = 2243 because this number is the first in a sequence of 3 consecutive primes all of the form 8n + 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, 8 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 9} ] a(9) > 305256000.

%Y Cf. A363017 (indices), A057624 (with 1 modulo 4).

%K nonn,more

%O 1,1

%A _Robert G. Wilson v_, Oct 10 2000

%E More terms from _Jens Kruse Andersen_, May 28 2006

%E a(16)-a(18) from _Giovanni Resta_, Aug 04 2013

%E a(19)-a(20) from _Martin Ehrenstein_, May 28 2023