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A323139 Integers that are not multiples of 6 and are the sum of two consecutive primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 19 04:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)