A323139 - OEIS

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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

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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;