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Search: id:A057619
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| A057619 |
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Initial prime in first sequence of n primes congruent to 3 modulo 4. |
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+0
4
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| 3, 7, 199, 199, 463, 463, 463, 36551, 39607, 183091, 241603, 241603, 241603, 9177431, 9177431, 95949311, 105639091, 341118307, 727334879, 727334879, 1786054147, 1786054147, 22964264027, 54870713243, 79263248027, 113391385603
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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R. K. Guy, "Unsolved Problems in Number Theory", A4
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LINKS
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J. K. Andersen, Consecutive Congruent Primes.
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EXAMPLE
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a(13) = 241603 because this number is the first in a sequence of 13 consecutive primes all of the form 4n + 3.
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MATHEMATICA
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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, 4 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 18} ]
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CROSSREFS
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Cf. A057620, A057622, A057624.
Sequence in context: A128273 A105763 A132564 this_sequence A061422 A088097 A064774
Adjacent sequences: A057616 A057617 A057618 this_sequence A057620 A057621 A057622
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 09 2000
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EXTENSIONS
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More terms from Don Reble (djr(AT)nk.ca), Nov 16 2003
More terms from Jens Kruse Andersen (jens.k.a(AT)get2net.dk), May 29 2006
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