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 1-3 of 3 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

A380572 Complement of A380509.

Original entry on oeis.org

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

Views

Author

Davide Rotondo, Jan 27 2025

Keywords

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

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

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

Original entry on oeis.org

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

Views

Author

Peter Bala, Jan 26 2025

Keywords

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;
Showing 1-3 of 3 results.

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

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