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A057631 Initial prime in first sequence of n primes congruent to 3 modulo 5. 2
3, 283, 6793, 22963, 752023, 2707163, 44923183, 44923183, 961129823, 1147752443, 6879806623, 131145172583, 177746482483, 795537219143, 4028596340953, 6987191424553, 269013937530553, 281659318133953, 281659318133953 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Carlos Rivera's The prime puzzles & problems connection, Puzzle 16 - Consecutive primes and ending digit

LINKS

Table of n, a(n) for n=1..19.

J. K. Andersen, Consecutive Congruent Primes.

EXAMPLE

a(6) = 2707163 because this number is the first in a sequence of 6 consecutive primes all of the form 5n + 3.

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 ] != {3}, 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

Sequence in context: A239273 A054583 A139984 * A058455 A116532 A199644

Adjacent sequences:  A057628 A057629 A057630 * A057632 A057633 A057634

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Oct 10 2000

EXTENSIONS

a(10) from Jud McCranie, Jan 14 2003

More terms from Jens Kruse Andersen, Jun 03 2006

a(17)-a(19) from Giovanni Resta, Aug 04 2013

STATUS

approved

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Last modified December 22 06:09 EST 2014. Contains 252328 sequences.