A057632 Initial prime in first sequence of n primes congruent to 3 modulo 8.
3, 491, 2243, 42299, 274123, 4310083, 4310083, 9065867, 547580443, 1885434347, 8674616939, 11312238283, 19201563659, 619849118491, 4056100954547, 13721202685691, 119254168189363, 276151474703651, 2189798979924331, 3153425741761723
Offset: 1
Examples
a(3) = 2243 because this number is the first in a sequence of 3 consecutive primes all of the form 8*n + 3.
Links
- J. K. Andersen, Consecutive Congruent Primes.
Programs
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Mathematica
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} ]
Extensions
More terms from Jens Kruse Andersen, May 28 2006
a(16)-a(18) from Giovanni Resta, Aug 04 2013
a(19)-a(20) from Martin Ehrenstein, May 28 2023