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A145993
Primes that start a run of at least 2 consecutive primes of the form 4k+3.
5
7, 19, 43, 67, 79, 103, 127, 163, 199, 307, 359, 379, 439, 463, 619, 643, 683, 719, 739, 823, 859, 883, 967, 983, 1087, 1163, 1279, 1303, 1423, 1439, 1459, 1483, 1499, 1559, 1663, 1783, 1811, 1867, 1979, 1999, 2083, 2099, 2179, 2239, 2347, 2399, 2447, 2531, 2579, 2659, 2683, 2699, 2803, 2843, 2879
OFFSET
1,1
REFERENCES
Enoch Haga, Exploring Primes on Your PC and the Internet, 1994-2007. Pp. 30-31. ISBN 978-1-885794-24-6
EXAMPLE
a(1)=7 because this sequence includes consecutive runs of any length and this first term >1 in a run of 2 is 7.
MAPLE
A145993 := proc()
local m, p, r, i, sp ;
m := 3 ;
p := 2 ;
r := 0 ;
sp := -1 ;
for i from 2 to 1000 do
if modp(p, 4) = m then
r := r+1 ;
if r = 1 then
sp := p ;
end if;
else
if r > 1 then
printf("%d, ", sp) ;
end if;
r := 0;
sp := -1 ;
end if;
p := nextprime(p) ;
end do:
end proc:
A145993() ; # R. J. Mathar, Aug 29 2018
MATHEMATICA
Most[First /@ Select[ SplitBy[ Prime@ Range@ 425, Mod[#, 4] &], Mod[#[[1]], 4] == 3 && Length[#] > 1 &]] (* Giovanni Resta, Aug 29 2018 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Enoch Haga, Oct 26 2008
EXTENSIONS
619 inserted by R. J. Mathar, Aug 29 2018
STATUS
approved