A323138 -id:A323138 - cp's OEIS frontend

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

5, 8, 52, 68, 100, 112, 128, 152, 172, 268, 308, 320, 340, 352, 410, 434, 472, 508, 520, 532, 548, 668, 712, 740, 752, 772, 872, 892, 946, 1012, 1030, 1064, 1088, 1120, 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

Offset: 1

Pedro Caceres, Jan 05 2019

nonn

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.

			52 = 23 + 29 is not a multiple of 6.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001043, A047253, A323138.

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

Select[Total /@ Partition[Prime@ Range@ 180, 2, 1], Mod[#, 6] != 0 &] (* Michael De Vlieger, Jan 07 2019 *)

my(p=2); forprime(q=3, 1e3, if ((p+q) % 6, print1(p+q", ")); p=q); \\ Michel Marcus, Jan 05 2019

cp's OEIS Frontend

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

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