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A323139 Integers that are not multiples of 6 and are the sum of two consecutive primes.

%I A323139 #26 Jan 23 2019 11:04:08
%S A323139 5,8,52,68,100,112,128,152,172,268,308,320,340,352,410,434,472,508,
%T A323139 520,532,548,668,712,740,752,772,872,892,946,1012,1030,1064,1088,1120,
%U A323139 1132,1148,1180,1192,1208,1220,1250,1300,1312,1334,1360,1460,1472,1508,1606,1888,1900,1948,1960,1988,2006,2032,2072,2132,2156
%N A323139 Integers that are not multiples of 6 and are the sum of two consecutive primes.
%C A323139 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.
%H A323139 Robert Israel, <a href="/A323139/b323139.txt">Table of n, a(n) for n = 1..10000</a>
%e A323139 52 = 23 + 29 is not a multiple of 6.
%p A323139 p:= 2:
%p A323139 count:= 0: Res:= NULL:
%p A323139 while count < 100 do
%p A323139   q:= nextprime(p);
%p A323139   if p+q mod 6 <> 0 then
%p A323139      count:= count+1; Res:= Res, p+q;
%p A323139   fi;
%p A323139   p:= q;
%p A323139 od:
%p A323139 Res; # _Robert Israel_, Jan 09 2019
%t A323139 Select[Total /@ Partition[Prime@ Range@ 180, 2, 1], Mod[#, 6] != 0 &] (* _Michael De Vlieger_, Jan 07 2019 *)
%o A323139 (PARI) my(p=2); forprime(q=3, 1e3, if ((p+q) % 6, print1(p+q", ")); p=q); \\ _Michel Marcus_, Jan 05 2019
%Y A323139 Cf. A001043, A047253, A323138.
%K A323139 nonn
%O A323139 1,1
%A A323139 _Pedro Caceres_, Jan 05 2019