A380550 List of numbers not of the form i + 3*j + 4*i*j for i, j >= 1.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 16, 17, 19, 20, 21, 25, 26, 27, 30, 31, 32, 34, 37, 39, 40, 41, 44, 45, 47, 49, 52, 54, 55, 56, 59, 62, 65, 66, 67, 70, 72, 75, 76, 77, 81, 82, 84, 86, 89, 91, 94, 95, 102, 104, 107, 109, 110, 111, 115, 116, 117, 119, 121, 122, 124, 125, 129, 130, 135, 136, 140, 142, 144, 146, 147, 149

Offset: 1

Author

Peter Bala, Jan 26 2025

Keywords

• nonn
• easy

Comments

This is a companion sequence to A380572. It is the complementary sequence to A380549.

Compare with A006093, numbers not of the form i + j + i*j, and A005097, numbers not of the form i + j + 2*i*j.

Apart from a(6) = 6, this sequence consists of all the positive integers N such that 4*N + 3 is either a prime or three times a prime.

Examples

			Factorization of 4*a(n) + 3 for n = 1..78:
[7,  11, 3*5, 19, 23, 3^3, 31, 3*13, 43, 47, 3*17, 59, 67, 71, 79, 83, 3*29, 103, 107, 3*37, 3*41, 127, 131, 139, 151, 3*53, 163, 167, 179, 3*61, 191, 199, 211, 3*73, 223, 227, 239, 251, 263, 3*89, 271, 283, 3*97, 3*101, 307, 311, 3*109, 331, 3*113, 347, 359, 367, 379, 383, 3*137, 419, 431, 439, 443, 3*149, 463, 467, 3*157, 479, 487, 491, 499, 503, 3*173, 523, 3*181, 547, 563, 571, 3*193, 587, 3*197, 599]
		

Links

• Peter Bala, 4*A380550(n) + 3 is either a prime or three times a prime except when n = 6

Crossrefs

Cf. A005097, A006093, A380549, A380572.

Programs

Maple

L := 150: N := {seq(n, n= 1..L)}: 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:
N minus S;