OFFSET
1,1
COMMENTS
The sequence is infinite, by Shiu's theorem. - Jonathan Sondow, Jun 22 2017
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, A4.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, Penguin Books, London, England, 1997, page 163.
LINKS
Jens Kruse Andersen, Consecutive Congruent Primes.
D. K. L. Shiu, Strings of Congruent Primes, J. Lond. Math. Soc. 61 (2) (2000) 359-373 [MR1760689]
EXAMPLE
a(9) = 11593 because "[t]his number is the first in a sequence of 9 consecutive primes all of the form 4n + 1."
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 ] != {1}, k = NextPrime[ k ]; a = Take[ AppendTo[ a, Mod[ k, 4 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 19} ]
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Robert G. Wilson v, Oct 09 2000
EXTENSIONS
More terms from Don Reble, Nov 16 2003
More terms from Jens Kruse Andersen, May 29 2006
STATUS
approved