A057634 Initial prime in first sequence of n primes congruent to 7 modulo 8.

7, 359, 1823, 79063, 272863, 989647, 10604519, 10604519, 309202951, 309202951, 1383423311, 21120585463, 534956098463, 534956098463, 534956098463, 925195153703, 74587805307479

Offset

1,1

Links

Table of n, a(n) for n=1..17.

J. K. Andersen, Consecutive Congruent Primes.

Example

a(4) = 79063 because this number is the first in a sequence of 4 consecutive primes all of the form 8*n + 7.

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 ] != {7}, k = NextPrime[ k ]; a = Take[ AppendTo[ a, Mod[ k, 8 ]], -n ]]; p = NestList[ PrevPrime, k, n ]; Print[ p[[ -2 ] ]]; p = p[[ -1 ]], {n, 1, 8} ]
With[{pm8=Table[If[Mod[p, 8]==7, 1, 0], {p, Prime[Range[16730000]]}]}, Prime[#]&/@Table[SequencePosition[pm8, PadRight[{}, n, 1], 1], {n, 10}]][[;; , 1, 1]] (* The program generates the first 10 terms of the sequence. *) (* Harvey P. Dale, Dec 12 2025 *)

Crossrefs

Sequence in context: A185062 A067556 A082098 * A385530 A203706 A145181

Adjacent sequences: A057631 A057632 A057633 * A057635 A057636 A057637

Keyword

nonn,more

Author

Robert G. Wilson v, Oct 10 2000

Extensions

More terms from Jens Kruse Andersen, May 28 2006

a(17) from Giovanni Resta, Aug 04 2013

Status

approved