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A057633
Initial prime in first sequence of n primes congruent to 5 modulo 8.
0
5, 389, 2213, 45013, 73133, 1319861, 3250469, 29662253, 35677501, 101341613, 12664911341, 12664911341, 124809839701, 132932904029, 1181960064853, 20151469541389, 20151469541389, 20151469541389, 102573904861013
OFFSET
1,1
EXAMPLE
a(3) = 2213 because this number is the first in a sequence of 3 consecutive primes all of the form 8n + 5.
MATHEMATICA
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 ] != {5}, 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} ]
Prime[#[[1, 1]]]&/@Table[SequencePosition[Table[If[Mod[Prime[n], 8]==5, 1, 0], {n, 6*10^6}], PadRight[{}, i, 1], 1], {i, 10}] (* The program uses the SequencePosition function from Mathematica version 10. It generates only the first ten terms. It could be modified to generate more but it would take increasingly lengthy times to generate the higher terms. *)
CROSSREFS
Sequence in context: A152438 A060506 A302394 * A193126 A006700 A079011
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Oct 10 2000
EXTENSIONS
More terms from Jens Kruse Andersen, May 28 2006
a(16)-a(19) from Giovanni Resta, Aug 04 2013
STATUS
approved