OFFSET
1,1
COMMENTS
All primes, except 2 and 3, are of the form 6k+1 or 6k-1 for k a positive integer. The converse statement is not true for all k, so the sum of two consecutive primes is not always a multiple of 6. This sequence lists the sums of two consecutive primes that are not multiple of 6.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
52 = 23 + 29 is not a multiple of 6.
MAPLE
p:= 2:
count:= 0: Res:= NULL:
while count < 100 do
q:= nextprime(p);
if p+q mod 6 <> 0 then
count:= count+1; Res:= Res, p+q;
fi;
p:= q;
od:
Res; # Robert Israel, Jan 09 2019
MATHEMATICA
Select[Total /@ Partition[Prime@ Range@ 180, 2, 1], Mod[#, 6] != 0 &] (* Michael De Vlieger, Jan 07 2019 *)
PROG
(PARI) my(p=2); forprime(q=3, 1e3, if ((p+q) % 6, print1(p+q", ")); p=q); \\ Michel Marcus, Jan 05 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Pedro Caceres, Jan 05 2019
STATUS
approved