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.

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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

A295748 Numbers that have exactly seven representations of a sum of seven nonnegative squares.

Original entry on oeis.org

25, 28, 31, 35
Offset: 1

Views

Author

Robert Price, Nov 26 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 two more zero squares, 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

A295151 Numbers that have exactly three representations as a sum of five nonnegative squares.

Original entry on oeis.org

13, 16, 17, 18, 19, 21, 22, 30, 31, 33, 39
Offset: 1

Views

Author

Robert Price, Nov 15 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, 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

A295152 Numbers that have exactly four representations as a sum of five nonnegative squares.

Original entry on oeis.org

20, 25, 26, 27, 28, 32, 47, 48, 60
Offset: 1

Views

Author

Robert Price, Nov 15 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, 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

A295154 Numbers that have exactly six representations as a sum of five nonnegative squares.

Original entry on oeis.org

37, 43, 45, 49, 51, 56, 63, 71, 96
Offset: 1

Views

Author

Robert Price, Nov 15 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, 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

A295155 Numbers that have exactly seven representations as a sum of five nonnegative squares.

Original entry on oeis.org

50, 54, 62, 64, 65, 69, 72, 78, 87
Offset: 1

Views

Author

Robert Price, Nov 15 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, 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

A295156 Numbers that have exactly eight representations as a sum of five nonnegative squares.

Original entry on oeis.org

52, 53, 58, 59, 66, 73, 79, 80, 81, 95, 105
Offset: 1

Views

Author

Robert Price, Nov 15 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, 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

Previous Showing 21-30 of 41 results. Next