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.

Previous Showing 11-15 of 15 results.

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

A295157 Numbers that have exactly nine representations as a sum of five nonnegative squares.

Original entry on oeis.org

61, 67, 68, 70, 75, 76, 84, 88, 89, 92, 120
Offset: 1

Views

Author

Robert Price, Nov 15 2017

Keywords

Comments

This sequence is finite and complete. See the von Eitzen Link. For positive integer n, if n > 6501 then the number of ways to write n as a sum of 5 squares is at least 10. So for n > 6501, there are more than eight ways to write n as a sum of 5 squares. For n <= 6501, it has been verified if n is in the sequence by inspection. Hence the sequence is complete.

References

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

Crossrefs

A295158 Numbers that have exactly ten representations as a sum of five nonnegative squares.

Original entry on oeis.org

74, 93, 97, 111
Offset: 1

Views

Author

Robert Price, Nov 15 2017

Keywords

Comments

This sequence is finite and complete. See the von Eitzen Link. For positive integer n, if n > 7845 then the number of ways to write n as a sum of 5 squares is at least 11. So for n > 7845, there are more than nine ways to write n as a sum of 5 squares. For n <= 7845, it has been verified if n is in the sequence by inspection. Hence the sequence is complete.

References

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

Crossrefs

Previous Showing 11-15 of 15 results.