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A179067
Orders of consecutive clusters of twin primes.
3
1, 3, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,2
COMMENTS
For k>=1, 2k+4 consecutive primes P1, P2, ..., P2k+4 defining a cluster of twin primes of order k iff P2-P1 <> 2, P4-P3 = P6-P5 = ... = P2k+2 - P2k+1 = 2, P2k+4 - P2k+3 <> 2.
LINKS
EXAMPLE
The twin prime cluster ((101,103),(107,109)) of order k=2 stems from the 2k+4 = 8 consecutive primes (89, 97, 101, 103, 107, 109, 113, 127) because 97-89 <> 2, 103-101 = 109-107 = 2, 127-113 <> 2.
MAPLE
R:= 1: count:= 1: m:= 0:
q:= 5: state:= 1:
while count < 100 do
p:= nextprime(q);
if state = 1 then
if p-q = 2 then state:= 2; m:= m+1;
else
if m > 0 then R:= R, m; count:= count+1; fi;
m:= 0
fi
else state:= 1;
fi;
q:= p
od:
R; # Robert Israel, Feb 07 2023
PROG
(PARI) a(n)={my(o, P, L=vector(3)); n++; forprime(p=o=3, , L=concat(L[2..3], -o+o=p); L[3]==2||next; L[1]==2&&(P=concat(P, p))&&next; n--||return(#P); P=[p])} \\ M. F. Hasler, May 04 2015
KEYWORD
easy,nonn
AUTHOR
Franz Vrabec, Jun 27 2010
EXTENSIONS
More terms from M. F. Hasler, May 04 2015
STATUS
approved