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A057632
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Initial prime in first sequence of n primes congruent to 3 modulo 8.
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1
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3, 491, 2243, 42299, 274123, 4310083, 4310083, 9065867, 547580443, 1885434347, 8674616939, 11312238283, 19201563659, 619849118491, 4056100954547, 13721202685691, 119254168189363, 276151474703651, 2189798979924331, 3153425741761723
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(3) = 2243 because this number is the first in a sequence of 3 consecutive primes all of the form 8n + 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, 8 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 9} ] a(9) > 305256000.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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