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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS J. K. Andersen, Consecutive Congruent Primes. 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 Adjacent sequences:  A057630 A057631 A057632 * A057634 A057635 A057636 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

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Last modified January 23 13:40 EST 2020. Contains 331171 sequences. (Running on oeis4.)