cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A380509 Numbers of the form i+j+4ij for i,j >= 1 together with numbers of the form -i-j+4ij for i,j >= 2.

Original entry on oeis.org

6, 11, 12, 16, 19, 20, 21, 26, 29, 30, 31, 33, 36, 38, 40, 41, 42, 46, 47, 51, 52, 54, 55, 56, 61, 63, 65, 66, 68, 71, 72, 74, 75, 76, 81, 82, 83, 85, 86, 89, 90, 91, 92, 94, 96, 101, 103, 106, 107, 109, 110, 111, 116, 117, 118, 119, 120, 121, 123, 124, 126, 128, 129, 131, 132, 133
Offset: 1

Views

Author

Davide Rotondo, Jan 26 2025

Keywords

Examples

			1+1+4*1*1 = 6; -2-2+4*2*2 = 12.

Crossrefs

Cf. A054520, A380140, A380572 (complement), A380549, A380550.

Programs

  • Maple
    L := 150: S := {}:
for i to L do for j to L do
if 4*i*j + i + j <= L then S := `union`(S, {4*i*j+i+j}, {4*i*j+3*i+3*j+2}) fi;
od; od;
S; # Peter Bala, Jan 30 2025

Extensions

More terms from Stefano Spezia, Jan 26 2025
Missing terms 111, 121 and 126 added by Peter Bala, Jan 30 2025

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

Original entry on oeis.org

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

Views

Author

Peter Bala, Jan 26 2025

Keywords

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

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;
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.