A380572 Complement of A380509.

1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 14, 15, 17, 18, 22, 23, 24, 25, 27, 28, 32, 34, 35, 37, 39, 43, 44, 45, 48, 49, 50, 53, 57, 58, 59, 60, 62, 64, 67, 69, 70, 73, 77, 78, 79, 80, 84, 87, 88, 93, 95, 97, 98, 99, 100, 102, 104, 105, 108, 111, 112, 113, 114, 115, 122

Offset: 1

Author

Davide Rotondo, Jan 27 2025

Keywords

• nonn

Comments

4*a(n) + 1 or (4*a(n) + 1)/3 is a prime number.

Compare with A380550, numbers not of the form i + 3*j + 4*i*j. See also A006093, numbers not of the form i + j + i*j and A005097, numbers not of the form i + j + 2*i*j. - Peter Bala, Jan 30 2025

Links

• Peter Bala, 4*A380572(n) + 1 is either a prime or three times a prime

Crossrefs

Cf. A005097, A006093, A380509, A380550.

Programs

Maple

S := {}:
for n from 1 to 150 do
  if isprime(4*n+1) then S := `union`(S, {n}) fi;
  if type((4*n+1)*(1/3), integer) then if isprime((4*n+1)*(1/3)) then S := `union`(S, {n}) fi; fi;
end do:
S; # Peter Bala, Jan 30 2025