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, 140432294381, 140432294381

Offset: 1

Author

Robert G. Wilson v, Oct 09 2000

Keywords

• nonn

Comments

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

Examples

			a(12) = 1820111 because this number is the first in a sequence of 12 consecutive primes all of the form 3*n + 2.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..35 (terms < 4*10^14)
• J. K. Andersen, Consecutive Congruent Primes.

Crossrefs

Cf. A057622, A000040, A247967.

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, 3 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 18} ]

Formula

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

Extensions

More terms from Jens Kruse Andersen, May 30 2006