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A057626
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Initial prime in first sequence of n primes congruent to 2 modulo 5.
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1
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2, 337, 1627, 57427, 192637, 776257, 15328637, 70275277, 244650317, 452942827, 452942827, 73712513057, 319931193737, 2618698284817, 10993283241587, 54010894438097, 101684513099627, 196948379177587
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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a(5) = 192637 because this number is the first in a sequence of 5 consecutive primes all of the form 5n + 2.
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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 ] != {2}, 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} ]
Module[{nn=13410000, pr5}, pr5=Table[If[Mod[p, 5]==2, 1, 0], {p, Prime[Range[nn]]}]; Prime/@ Table[SequencePosition[pr5, PadRight[{}, n, 1], 1], {n, 8}]][[;; , 1, 1]] (* The program generates the first 8 terms of the sequence. *) (* Harvey P. Dale, Jan 07 2024 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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