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

1,1

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

Cf. A001043, A047253, A323138.

Sequence in context: A192379 A117474 A294665 * A284381 A165716 A068478

Adjacent sequences: A323136 A323137 A323138 * A323140 A323141 A323142

Keyword

nonn

Author

Pedro Caceres, Jan 05 2019

Status

approved