A057638 Initial prime in first sequence of n primes congruent to 1 modulo 8.

17, 89, 2593, 20809, 208393, 2663897, 7336457, 42453937, 42453937, 1506473153, 24771906961, 123737745289, 152368449001, 152368449001, 4990160038937, 50515057659673, 169068296123497, 402384411007849

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.
Module[{nn=75100000, pr8}, pr8=Table[If[Mod[p, 8]==1, 1, 0], {p, Prime[Range[nn]]}]; Prime[#]&/@Table[SequencePosition[ pr8, PadRight[ {}, n, 1], 1], {n, 10}]][[;; , 1, 1]] (* The program generates the first 10 terms of the sequence. *) (* Harvey P. Dale, Sep 29 2024 *)

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