OFFSET
1,1
COMMENTS
The term "exactly" means that before the first and after the last terms of the run, the next primes are not congruent to 1 modulo 4.
Carlos Rivera's Puzzle 256 includes Jack Brennen's a(29) starting at 689101181569 to 689101182437 and asks if anyone can break that 1999 record.
LINKS
J. K. Andersen, Consecutive Congruent Primes.
Carlos Rivera's Prime Puzzles and Problems Connection, Puzzle 256, Jack Brennen old records
FORMULA
Compute sequence of primes congruent to 1 mod 4. When first occurrence of run of exactly length n is found, add first prime to sequence.
EXAMPLE
a(3)=89 because here n=3 and 89 is the start of a run of exactly 3 consecutive primes congruent to 1 mod 4.
n=3: 83, 89, 97, 101, 103 are congruent to 3, 1, 1, 1, 3 modulo 4. So a(3) = 89.
a(33) = 3278744415797. - Jens Kruse Andersen, May 29 2006
MATHEMATICA
nn = 10; t = Table[0, {nn}]; found = 0; p = 1; cnt = 0; While[found < nn, p = NextPrime[p]; If[Mod[p, 4] == 1, cnt++, If[0 < cnt <= nn && t[[cnt]] == 0, t[[cnt]] = NextPrime[p, -cnt]; found++]; cnt = 0]]; t (* T. D. Noe, Jun 21 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 05 2000
EXTENSIONS
Corrected and extended by Reiner Martin, Jul 18 2001
More terms from Jens Kruse Andersen, May 29 2006
Edited by N. J. A. Sloane, Jun 01 2006
STATUS
approved