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A057621 Initial prime in first sequence of n primes congruent to 2 modulo 3. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 03:26 EST 2016. Contains 278755 sequences.