A323138 - OEIS

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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

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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 multiples of 6 that cannot be expressed as a sum of two consecutive primes.

LINKS

Table of n, a(n) for n=1..57.

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

Cf. A001043. Subsequence of A008588.

Sequence in context: A320403 A354067 A357430 * A000252 A078237 A274131

Adjacent sequences: A323135 A323136 A323137 * A323139 A323140 A323141

KEYWORD

nonn

AUTHOR

Pedro Caceres, Jan 05 2019

STATUS

approved