A395654 Numbers divisible by 6 that are not the sum of a member of A022004 and a member of A022005.

6, 36, 60, 66, 90, 96, 126, 132, 150, 156, 162, 180, 186, 192, 216, 222, 246, 252, 270, 276, 306, 336, 342, 366, 372, 390, 396, 402, 426, 432, 438, 456, 480, 486, 492, 510, 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

Offset

1,1

Comments

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.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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

Maple

N:= 1000: # for terms <= N
A4:= select(p -> isprime(p) and isprime(p+2) and isprime(p+6), [seq(i, i=5..N, 6)]):
A5:= select(p -> isprime(p) and isprime(p+4) and isprime(p+6), [seq(i, i=1..N, 6)]):
f:= proc(n) local p, q, v;
for p in A4 do
        q:= n-p;
        if q < 0 then return true fi;
        v:= ListTools:-BinarySearch(A5, q);
        if v <> 0 then return false fi;
      od;
 true
end proc:
select(f, [seq(i, i=6..N, 6)]);

Crossrefs

Cf. A022004, A022005, A396570.

Sequence in context: A047792 A178909 A206982 * A121026 A207694 A208496

Adjacent sequences: A395650 A395652 A395653 * A395655 A395656 A395657

Keyword

nonn

Author

Robert Israel, May 30 2026

Status

approved