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A057620
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Initial prime in first sequence of n primes congruent to 1 modulo 6.
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3
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7, 31, 151, 1741, 1741, 1741, 19471, 118801, 148531, 148531, 406951, 2339041, 2339041, 51662593, 51662593, 73451737, 232301497, 450988159, 1444257673, 1444257673, 1444257673, 24061965043, 24061965043, 43553959717, 43553959717
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| R. K. Guy, "Unsolved Problems in Number Theory", A4
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LINKS
| J. K. Andersen, Consecutive Congruent Primes.
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EXAMPLE
| a(6) = 1741 because this number is the first in a sequence of 6 consecutive primes all of the form 3n + 1.
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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 ] != {1}, 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} ]
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CROSSREFS
| Cf. A057619, A057622, A057624.
Sequence in context: A003526 A121517 A199216 * A055625 A102239 A188233
Adjacent sequences: A057617 A057618 A057619 * A057621 A057622 A057623
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 09 2000
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EXTENSIONS
| 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 30 2006
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