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 1-10 of 10 results.

A295489 Numbers that have exactly six representations as a sum of six nonnegative squares.

Original entry on oeis.org

30, 33, 34, 35, 39, 40
Offset: 1

Views

Author

Robert Price, Nov 22 2017

Keywords

Comments

This sequence is finite and complete. See the von Eitzen Link and the proof in A294675 stating that for n > 5408, the number of ways to write n as a sum of 5 squares (without allowing zero squares) is at least floor(sqrt(n - 101) / 8) = 9. Since this sequence relaxes the restriction of zero squares and allows one more square, the number of representations for n > 5408 is at least nine. Then an inspection of n <= 5408 completes the proof.

References

  • E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.

Crossrefs

A295485 Numbers that have exactly two representations as a sum of six nonnegative squares.

Original entry on oeis.org

4, 5, 6, 8, 10, 11, 15
Offset: 1

Views

Author

Robert Price, Nov 22 2017

Keywords

Comments

This sequence is finite and complete. See the von Eitzen Link and the proof in A294675 stating that for n > 5408, the number of ways to write n as a sum of 5 squares (without allowing zero squares) is at least floor(sqrt(n - 101) / 8) = 9. Since this sequence relaxes the restriction of zero squares and allows one more square, the number of representations for n > 5408 is at least nine. Then an inspection of n <= 5408 completes the proof.

References

  • E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.

Crossrefs

A295486 Numbers that have exactly three representations as a sum of six nonnegative squares.

Original entry on oeis.org

9, 12, 13, 14, 16, 19, 23
Offset: 1

Views

Author

Robert Price, Nov 22 2017

Keywords

Comments

This sequence is finite and complete. See the von Eitzen Link and the proof in A294675 stating that for n > 5408, the number of ways to write n as a sum of 5 squares (without allowing zero squares) is at least floor(sqrt(n - 101) / 8) = 9. Since this sequence relaxes the restriction of zero squares and allows one more square, the number of representations for n > 5408 is at least nine. Then an inspection of n <= 5408 completes the proof.

References

  • E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.

Crossrefs

A295487 Numbers that have exactly four representations as a sum of six nonnegative squares.

Original entry on oeis.org

17, 18, 22, 24, 31
Offset: 1

Views

Author

Robert Price, Nov 22 2017

Keywords

Comments

This sequence is finite and complete. See the von Eitzen Link and the proof in A294675 stating that for n > 5408, the number of ways to write n as a sum of 5 squares (without allowing zero squares) is at least floor(sqrt(n - 101) / 8) = 9. Since this sequence relaxes the restriction of zero squares and allows one more square, the number of representations for n > 5408 is at least nine. Then an inspection of n <= 5408 completes the proof.

References

  • E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.

Crossrefs

A295488 Numbers that have exactly five representations as a sum of six nonnegative squares.

Original entry on oeis.org

20, 21, 25, 26, 27, 28, 32
Offset: 1

Views

Author

Robert Price, Nov 22 2017

Keywords

Comments

This sequence is finite and complete. See the von Eitzen Link and the proof in A294675 stating that for n > 5408, the number of ways to write n as a sum of 5 squares (without allowing zero squares) is at least floor(sqrt(n - 101) / 8) = 9. Since this sequence relaxes the restriction of zero squares and allows one more square, the number of representations for n > 5408 is at least nine. Then an inspection of n <= 5408 completes the proof.

References

  • E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.

Crossrefs

A295490 Numbers that have exactly seven representations as a sum of six nonnegative squares.

Original entry on oeis.org

29, 37, 42, 43, 47, 48
Offset: 1

Views

Author

Robert Price, Nov 22 2017

Keywords

Comments

This sequence is finite and complete. See the von Eitzen Link and the proof in A294675 stating that for n > 5408, the number of ways to write n as a sum of 5 squares (without allowing zero squares) is at least floor(sqrt(n - 101) / 8) = 9. Since this sequence relaxes the restriction of zero squares and allows one more square, the number of representations for n > 5408 is at least nine. Then an inspection of n <= 5408 completes the proof.

References

  • E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.

Crossrefs

A295491 Numbers that have exactly eight representations as a sum of six nonnegative squares.

Original entry on oeis.org

38, 46, 55
Offset: 1

Views

Author

Robert Price, Nov 22 2017

Keywords

Comments

This sequence is finite and complete. See the von Eitzen Link and the proof in A294675 stating that for n > 5408, the number of ways to write n as a sum of 5 squares (without allowing zero squares) is at least floor(sqrt(n - 101) / 8) = 9. Since this sequence relaxes the restriction of zero squares and allows one more square, the number of representations for n > 5408 is at least nine. Then an inspection of n <= 5408 completes the proof.

References

  • E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.

Crossrefs

A295492 Numbers that have exactly nine representations as a sum of six nonnegative squares.

Original entry on oeis.org

36, 41, 44, 49, 51, 64
Offset: 1

Views

Author

Robert Price, Nov 22 2017

Keywords

Comments

This sequence is finite and complete. See the von Eitzen Link and the proof in A294675 stating that for n > 6501, the number of ways to write n as a sum of 5 squares (without allowing zero squares) is at least 10. Since this sequence relaxes the restriction of zero squares and allows one more square, the number of representations for n > 6501 is at least ten. Then an inspection of n <= 6501 completes the proof.

References

  • E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.

Crossrefs

A295493 Numbers that have exactly ten representations as a sum of six nonnegative squares.

Original entry on oeis.org

45, 50, 56, 58
Offset: 1

Views

Author

Robert Price, Nov 22 2017

Keywords

Comments

This sequence is finite and complete. See the von Eitzen Link and the proof in A294675 stating that for n > 7845, the number of ways to write n as a sum of 5 squares (without allowing zero squares) is at least 11. Since this sequence relaxes the restriction of zero squares and allows one more square, the number of representations for n > 7845 is at least 11. Then an inspection of n <= 7845 completes the proof.

References

  • E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.

Crossrefs

A295484 Numbers that have exactly one representation as a sum of six nonnegative squares.

Original entry on oeis.org

0, 1, 2, 3, 7
Offset: 1

Views

Author

Robert Price, Nov 22 2017

Keywords

Comments

This sequence is finite and complete. See the von Eitzen Link and the proof in A294675 stating that for n > 5408, the number of ways to write n as a sum of 5 squares (without allowing zero squares) is at least floor(sqrt(n - 101) / 8) = 9. Since this sequence relaxes the restriction of zero squares and allows one more square, the number of representations for n > 5408 is at least nine. Then an inspection of n <= 5408 completes the proof.

References

  • E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.

Crossrefs

Showing 1-10 of 10 results.