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.

A368418 Numbers X such that X^2 + Y^2 = 10^(2*k) + 1, with X > Y > 0 and k is the decimal digit length of X-1.

Original entry on oeis.org

10, 76, 100, 980, 1000, 8824, 10000, 76249, 87551, 98020, 100000, 753424, 766424, 999800, 1000000, 7209049, 7241380, 8220640, 8463640, 9801980, 9879740, 9990280, 10000000, 77053825, 78173720, 80404255, 83754376, 84711551, 86600176, 90880001, 93094625, 93728480
Offset: 1

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Author

A.H.M. Smeets, Dec 24 2023

Keywords

Comments

The values X and Y are used in finding A368416.
The number of terms for a given k is 2^(f-1), where f = A119704(2*k) is the number of prime factors of 10^(2*k) + 1.

Examples

			10 is a term since X = 10, Y = 1, k = 1 and 10^2 + 1^2 = 101.
76 is a term since X = 76, Y = 65, k = 2 and 76^2 + 65^2 = 10001.
980 is a term since X = 980, Y = 199, k = 3 and 980^2 + 199^2 = 1000001.
		

References

  • Frits Beukers, "Getallen - Een inleiding" (In Dutch), Epsilon Uitgaven, Amsterdam (2015).

Crossrefs