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Search: id:A057618
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| A057618 |
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Initial prime in first sequence of n primes congruent to 1 modulo 5. |
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+0
3
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| 11, 181, 4831, 22501, 216401, 2229971, 3873011, 36539311, 36539311, 196943081, 14293856441, 154351758091, 154351758091, 154351758091
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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Carlos Rivera's The prime puzzles & problems connection, Puzzle 16 - Consecutive primes and ending digit
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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(6) = 2229971 because this number is the first in a sequence of 6 consecutive primes all of the form 5n + 1.
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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 ] != {1}, k = NextPrime[ k ]; a = Take[ AppendTo[ a, Mod[ k, 5 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 10} ]
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CROSSREFS
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Cf. A054681.
Sequence in context: A143413 A009118 A112943 this_sequence A068648 A034787 A001408
Adjacent sequences: A057615 A057616 A057617 this_sequence A057619 A057620 A057621
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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 Jens Kruse Andersen (jens.k.a(AT)get2net.dk), Jun 03 2006
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