A057626 Initial prime in first sequence of n primes congruent to 2 modulo 5.

2, 337, 1627, 57427, 192637, 776257, 15328637, 70275277, 244650317, 452942827, 452942827, 73712513057, 319931193737, 2618698284817, 10993283241587, 54010894438097, 101684513099627, 196948379177587

Offset: 1

Author

Robert G. Wilson v, Oct 09 2000

Keywords

• nonn

Comments

Same as A068150 except a(1). - Jens Kruse Andersen, Jun 03 2006

Examples

			a(5) = 192637 because this number is the first in a sequence of 5 consecutive primes all of the form 5n + 2.
		

Links

• J. K. Andersen, Consecutive Congruent Primes.

Programs

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, 5 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 9} ]
Module[{nn=13410000,pr5},pr5=Table[If[Mod[p,5]==2,1,0],{p,Prime[Range[nn]]}];Prime/@ Table[SequencePosition[pr5,PadRight[{},n,1],1],{n,8}]][[;;,1,1]] (* The program generates the first 8 terms of the sequence. *) (* Harvey P. Dale, Jan 07 2024 *)

Extensions

More terms from Jens Kruse Andersen, Jun 03 2006

a(15)-a(18) from Giovanni Resta, Aug 04 2013