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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

Table of n, a(n) for n=1..19.

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.)