A057621 Initial prime in first sequence of n primes congruent to 2 modulo 3.

2, 23, 47, 251, 1889, 7793, 43451, 243161, 726893, 759821, 1820111, 1820111, 10141499, 19725473, 19725473, 136209239, 400414121, 400414121, 489144599, 489144599, 766319189, 766319189, 21549657539, 21549657539, 21549657539

Offset

1,1

Comments

Same as A057622 except for a(1). - Jens Kruse Andersen, May 30 2006

Links

Giovanni Resta, Table of n, a(n) for n = 1..35 (terms < 4*10^14)

J. K. Andersen, Consecutive Congruent Primes.

Formula

a(n) = A000040(A247967(n)) for all n > 1. - M. F. Hasler, Sep 03 2016

Example

a(12) = 1820111 because this number is the first in a sequence of 12 consecutive primes all of the form 3n + 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, 3 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 18} ] a(19) > 434562473.

Crossrefs

Sequence in context: A139831 A049592 A054679 * A074809 A084237 A106928

Adjacent sequences: A057618 A057619 A057620 * A057622 A057623 A057624

Keyword

nonn

Author

Robert G. Wilson v, Oct 09 2000

Extensions

More terms from Jens Kruse Andersen, May 30 2006

Status

approved