A057636 Initial prime in first sequence of n primes congruent to 4 modulo 5. The first prime in a sequence of length n all ending with the digit 9.

19, 139, 3089, 18839, 123229, 2134519, 12130109, 23884639, 363289219, 9568590299, 24037796539, 130426565719, 405033487139, 3553144754209, 4010803176619, 71894236537009, 71894236537009

Offset: 1

Author

Robert G. Wilson v, Oct 10 2000

Keywords

• nonn

Examples

			a(5) = 123229 because this number is the first in a sequence of 5 consecutive primes all of the form 5n + 4.
		

Links

• J. K. Andersen, Consecutive Congruent Primes.

Crossrefs

Cf. A054681, A057618, A057631, A068150.

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 ] != {4}, 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} ]

Extensions

Phil Carmody gives a(15)= 4010803176619 in A054681

More terms from Jens Kruse Andersen, Jun 03 2006

a(16)-a(17) from Giovanni Resta, Aug 01 2013