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A057638 Initial prime in first sequence of n primes congruent to 1 modulo 8. 0
17, 89, 2593, 20809, 208393, 2663897, 7336457, 42453937, 42453937, 1506473153, 24771906961, 123737745289, 152368449001, 152368449001, 4990160038937, 50515057659673, 169068296123497, 402384411007849 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..18.

J. K. Andersen, Consecutive Congruent Primes.

EXAMPLE

a(4) = 20809 because this number is the first in a sequence of 4 consecutive primes all of the form 8n + 1.

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 ] != {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.

CROSSREFS

Sequence in context: A138338 A267820 A200670 * A159676 A061971 A061222

Adjacent sequences:  A057635 A057636 A057637 * A057639 A057640 A057641

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Oct 10 2000

EXTENSIONS

More terms from Jens Kruse Andersen, May 28 2006

a(16)-a(18) from Giovanni Resta, Aug 04 2013

STATUS

approved

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Last modified January 25 01:39 EST 2020. Contains 331229 sequences. (Running on oeis4.)