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A323138 Multiples of 6 that are not the sum of two consecutive primes. 1
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 (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 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: A192887 A321190 A320403 * A000252 A078237 A274131

Adjacent sequences:  A323135 A323136 A323137 * A323139 A323140 A323141

KEYWORD

nonn

AUTHOR

Pedro Caceres, Jan 05 2019

STATUS

approved

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Last modified July 15 16:29 EDT 2019. Contains 325049 sequences. (Running on oeis4.)