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Search: id:A057636
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| A057636 |
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Initial prime in first sequence of n primes congruent to 4 modulo 5. The first prime in a sequence of length n all ending with the digit 9. |
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+0
1
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| 19, 139, 3089, 18839, 123229, 2134519, 12130109, 23884639, 363289219, 9568590299, 24037796539, 130426565719, 405033487139, 3553144754209, 4010803176619
(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(5) = 123229 because this number is the first in a sequence of 5 consecutive primes all of the form 5n + 4.
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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 ] != {4}, 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} ]
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CROSSREFS
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Cf. A054681, A057618, A057631, A068150.
Sequence in context: A142746 A139902 A140624 this_sequence A104046 A060104 A110694
Adjacent sequences: A057633 A057634 A057635 this_sequence A057637 A057638 A057639
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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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Phil Carmody gives a(15)= 4010803176619 in A054681
More terms from Jens Kruse Andersen (jens.k.a(AT)get2net.dk), Jun 03 2006
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