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

1,1

Links

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

J. K. Andersen, Consecutive Congruent Primes.

Example

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

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} ]

Crossrefs

Cf. A054681, A057618, A057631, A068150.

Sequence in context: A140624 A244505 A235146 * A104046 A060104 A201151

Adjacent sequences: A057633 A057634 A057635 * A057637 A057638 A057639

Keyword

nonn

Author

Robert G. Wilson v, Oct 10 2000

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

Status

approved