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

1,2

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

Table of n, a(n) for n=1..65.

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

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

Crossrefs

Cf. A005097, A006093, A380509, A380550.

Sequence in context: A175020 A050728 A230999 * A180590 A289342 A286302

Adjacent sequences: A380569 A380570 A380571 * A380575 A380581 A380582

Keyword

nonn

Author

Davide Rotondo, Jan 27 2025

Status

approved