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 11-13 of 13 results.

A294742 Numbers that are the sum of 5 nonzero squares in exactly 8 ways.

Original entry on oeis.org

91, 104, 106, 119, 122, 123, 126, 141, 143, 162, 185, 225
Offset: 1

Views

Author

Robert Price, Nov 07 2017

Keywords

Comments

Theorem: There are no further terms. Proof (from a proof by David A. Corneth on Nov 08 2017 in A294736): The von Eitzen link states that if n > 5408 then the number of ways to write n as a sum of 5 squares is at least floor(sqrt(n - 101) / 8) = 9. For n <= 5408, terms have been verified by inspection. Hence this sequence is finite and complete.

References

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

Crossrefs

Programs

  • Mathematica
    fQ[n_] := Block[{pr = PowersRepresentations[n, 5, 2]}, Length@Select[pr, #[[1]] > 0 &] == 8]; Select[Range@250, fQ] (* Robert G. Wilson v, Nov 17 2017 *)

A294743 Numbers that are the sum of 5 nonzero squares in exactly 9 ways.

Original entry on oeis.org

101, 112, 115, 118, 127, 144, 159, 161, 165, 169, 180
Offset: 1

Views

Author

Robert Price, Nov 07 2017

Keywords

Comments

Theorem: There are no further terms. Proof (from a proof by David A. Corneth on Nov 08 2017 in A294736): The von Eitzen link states that if n > 6501 then the number of ways to write n as a sum of 5 squares is at least 10. For n <= 6501 terms have been verified by inspection. Hence this sequence is finite and complete.

References

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

Crossrefs

Programs

  • Mathematica
    fQ[n_] := Block[{pr = PowersRepresentations[n, 5, 2]}, Length@Select[pr, #[[1]] > 0 &] == 9]; Select[Range@250, fQ](* Robert G. Wilson v, Nov 17 2017 *)

A294744 Numbers that are the sum of 5 nonzero squares in exactly 10 ways.

Original entry on oeis.org

107, 109, 116, 125, 140, 146, 168, 209, 249, 273, 297
Offset: 1

Views

Author

Robert Price, Nov 07 2017

Keywords

Comments

Theorem: There are no further terms. Proof (from a proof by David A. Corneth on Nov 08 2017 in A294736): The von Eitzen link states that if n > 7845 then the number of ways to write n as a sum of 5 squares is at least 11. For n <= 7845 terms have been verified by inspection. Hence this sequence is finite and complete.

References

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

Crossrefs

Programs

  • Mathematica
    fQ[n_] := Block[{pr = PowersRepresentations[n, 5, 2]}, Length@Select[pr, #[[1]] > 0 &] == 10]; Select[ Range@300, fQ](* Robert G. Wilson v, Nov 17 2017 *)
Previous Showing 11-13 of 13 results.