cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A323138 #18 Jan 11 2019 17:45:34
%S A323138 6,48,54,66,72,96,102,108,114,126,132,150,156,168,174,180,192,228,234,
%T A323138 246,252,264,270,282,294,306,312,318,324,336,342,348,354,366,378,402,
%U A323138 408,414,420,426,432,438,444,468,474,486,498,504,510,516,522,528,534,546,552,570,582
%N A323138 Multiples of 6 that are not the sum of two consecutive primes.
%C A323138 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.
%e A323138 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.
%t A323138 Complement[6 Range[Last[#]/6], #] &@ Select[Total /@ Partition[Prime@ Range@ 63, 2, 1], Mod[#, 6] == 0 &] (* _Michael De Vlieger_, Jan 07 2019 *)
%o A323138 (PARI) isok(n) = !(n % 6) && (precprime((n-1)/2) + nextprime(n/2) != n); \\ _Michel Marcus_, Jan 05 2019
%Y A323138 Cf. A001043. Subsequence of A008588.
%K A323138 nonn
%O A323138 1,1
%A A323138 _Pedro Caceres_, Jan 05 2019