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 multiples of 6 that cannot be expressed as a sum of two consecutive primes.
EXAMPLE
6 belongs to the sequence because there are no two consecutive primes adding up to 6. 12 is not in the sequence because 12 = 5 + 7.
MATHEMATICA
Complement[6 Range[Last[#]/6], #] &@ Select[Total /@ Partition[Prime@ Range@ 63, 2, 1], Mod[#, 6] == 0 &] (* Michael De Vlieger, Jan 07 2019 *)
PROG
(PARI) isok(n) = !(n % 6) && (precprime((n-1)/2) + nextprime(n/2) != n); \\ Michel Marcus, Jan 05 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Pedro Caceres, Jan 05 2019
STATUS
approved