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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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2
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11, 181, 4831, 22501, 216401, 2229971, 3873011, 36539311, 36539311, 196943081, 14293856441, 154351758091, 154351758091, 154351758091, 11992377039481, 41947964349971, 253931039382791, 253931039382791, 253931039382791
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OFFSET
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1,1
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COMMENTS
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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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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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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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