A395654 - OEIS

%I #8 Jun 03 2026 17:14:49

%S 6,36,60,66,90,96,126,132,150,156,162,180,186,192,216,222,246,252,270,

%T 276,306,336,342,366,372,390,396,402,426,432,438,456,480,486,492,510,

%U 516,522,546,552,576,582,594,600,606,612,636,642,660,666,672,690,696,702,726,732,750,756,762,774,780

%N Numbers divisible by 6 that are not the sum of a member of A022004 and a member of A022005.

%C Numbers k divisible by 6 such that there do not exist p and q such that p + q = k and p, p + 2, p + 6, q, q + 4 and q + 6 are all prime.

%H Robert Israel, <a href="/A395654/b395654.txt">Table of n, a(n) for n = 1..10000</a>

%e 54 is not a term because 54 = 17 + 37 where 17 is in A022004 and 37 is in A022005.

%e a(3) = 60 is a term because the members of A022004 less than 60 are 5, 11, 17, and 41, and none of 60 - 5 = 55, 60 - 11 = 49, 60 - 17 = 43 and 60 - 41 = 19 are in A022005.

%p N:= 1000: # for terms <= N

%p A4:= select(p -> isprime(p) and isprime(p+2) and isprime(p+6), [seq(i,i=5..N,6)]):

%p A5:= select(p -> isprime(p) and isprime(p+4) and isprime(p+6), [seq(i,i=1..N,6)]):

%p f:= proc(n) local p,q,v;

%p for p in A4 do

%p         q:= n-p;

%p         if q < 0 then return true fi;

%p         v:= ListTools:-BinarySearch(A5,q);

%p         if v <> 0 then return false fi;

%p       od;

%p  true

%p end proc:

%p select(f, [seq(i,i=6..N,6)]);

%Y Cf. A022004, A022005, A396570.

%K nonn

%O 1,1

%A _Robert Israel_, May 30 2026