A380549 List of numbers of the form i + 3*j + 4*i*j for i, j >= 1.

8, 13, 15, 18, 22, 23, 24, 28, 29, 33, 35, 36, 38, 42, 43, 46, 48, 50, 51, 53, 57, 58, 60, 61, 63, 64, 68, 69, 71, 73, 74, 78, 79, 80, 83, 85, 87, 88, 90, 92, 93, 96, 97, 98, 99, 100, 101, 103, 105, 106, 108, 112, 113, 114, 118, 120, 123, 126, 127, 128, 131, 132, 133, 134, 137, 138, 139, 141, 143, 145, 148, 150

Offset: 1

Author

Peter Bala, Jan 26 2025

Keywords

• nonn
• easy

Comments

This is a companion sequence to A380509. If N != 6 is a positive integer not in this list then 4*N + 3 is either a prime or three times a prime. See A380550.

Compare with A072668, numbers of the form i + j + i*j, and A047845, numbers of the form i + j + 2*i*j.

Crossrefs

Cf. A047845, A072668, A380509, A380550.

Programs

Maple

L := 150:  S := {}:
for i from 1 to L do
  for j from 1 to L do
    if i + 3*j + 4*i*j <= L then S := `union`(S, {i+3*j+4*i*j}) end if
  end do;
end do:
S;