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Search: id:A057638
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| A057638 |
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Initial prime in first sequence of n primes congruent to 1 modulo 8. |
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+0
1
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| 17, 89, 2593, 20809, 208393, 2663897, 7336457, 42453937, 42453937, 1506473153, 24771906961, 123737745289, 152368449001, 152368449001, 4990160038937
(list; graph; listen)
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OFFSET
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1,1
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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(4) = 20809 because this number is the first in a sequence of 4 consecutive primes all of the form 8n + 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, 8 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 9} ] a(10) > 123700000.
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CROSSREFS
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Sequence in context: A033654 A139947 A138338 this_sequence A061971 A061222 A119783
Adjacent sequences: A057635 A057636 A057637 this_sequence A057639 A057640 A057641
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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 10 2000
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EXTENSIONS
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More terms from Jens Kruse Andersen (jens.k.a(AT)get2net.dk), May 28 2006
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