A323138 Multiples of 6 that are not the sum of two consecutive primes.

6, 48, 54, 66, 72, 96, 102, 108, 114, 126, 132, 150, 156, 168, 174, 180, 192, 228, 234, 246, 252, 264, 270, 282, 294, 306, 312, 318, 324, 336, 342, 348, 354, 366, 378, 402, 408, 414, 420, 426, 432, 438, 444, 468, 474, 486, 498, 504, 510, 516, 522, 528, 534, 546, 552, 570, 582

Offset: 1

Author

Pedro Caceres, Jan 05 2019

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A001043. Subsequence of A008588.

Programs

Mathematica

Complement[6 Range[Last[#]/6], #] &@ Select[Total /@ Partition[Prime@ Range@ 63, 2, 1], Mod[#, 6] == 0 &] (* Michael De Vlieger, Jan 07 2019 *)

PARI

isok(n) = !(n % 6) && (precprime((n-1)/2) + nextprime(n/2) != n); \\ Michel Marcus, Jan 05 2019