A057645 Initial prime in first sequence of n primes congruent to 2 modulo 9.

2, 5483, 25373, 182243, 5379113, 5379113, 1734847733, 12196390601, 17619405959, 213529133423, 2732797330031

Offset

1,1

Links

Table of n, a(n) for n=1..11.

J. K. Andersen, Consecutive Congruent Primes.

Example

a(2) = 5483 because this number is the first in a sequence of 2 consecutive primes all of the form 9n + 2.

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 ] != {2}, k = NextPrime[ k ]; a = Take[ AppendTo[ a, Mod[ k, 9 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 6} ] a(7) > 331804250.
Prime[#]&/@Table[SequencePosition[Table[If[Mod[p, 9]==2, 1, 0], {p, Prime[Range[400000]]}], PadRight[{}, n, 1, 1], 1], {n, 6}][[;; , 1, 1]] (* The program generates the first 6 terms of the sequence. *) (* Harvey P. Dale, Jan 04 2025 *)

Crossrefs

Sequence in context: A153737 A078933 A064029 * A129060 A190127 A374194

Adjacent sequences: A057642 A057643 A057644 * A057646 A057647 A057648

Keyword

nonn

Author

Robert G. Wilson v, Oct 11 2000

Extensions

More terms from Jens Kruse Andersen, May 31 2006

Status

approved