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 1-3 of 3 results.

A230759 Values of x such that x^2 + y^2 = 53^n with x and y coprime and 0 < x < y.

Original entry on oeis.org

2, 28, 259, 1241, 3647, 14715, 399301, 4810319, 34161842, 146769868, 244200526, 4359995640, 73982566838, 804676166812, 4381447604821, 15981352647839, 8477785985767, 965700694136205, 13070487060661219, 114948480102611400, 541029996598203398
Offset: 1

Views

Author

Colin Barker, Oct 29 2013

Keywords

Comments

The corresponding y-values are in A230760.

Examples

			a(3)=259 because 259^2+286^2=148877=53^3.
		

Crossrefs

Programs

  • Mathematica
    Table[Select[PowersRepresentations[53^n, 2, 2], CoprimeQ@@#&][[1, 1]], {n, 1, 40}] (* Vincenzo Librandi, Mar 02 2014 *)

A230842 Values of y such that x^2 + y^2 = 61^n with x and y coprime and 0 < x < y.

Original entry on oeis.org

6, 60, 415, 3479, 27474, 194220, 1752665, 10361041, 108089046, 665045051, 6449019055, 45629658360, 371682946434, 3000926368429, 20605153668425, 190323205453920, 1089586196530086, 11672337637546091, 73603293662217846, 692487869011494600, 5011061854350480605
Offset: 1

Views

Author

Colin Barker, Oct 31 2013

Keywords

Comments

The corresponding x-values are in A230841.

Examples

			a(3)=415 because 234^2+415^2=226981=61^3.
		

Crossrefs

Programs

  • Mathematica
    Table[Select[PowersRepresentations[61^n, 2, 2], CoprimeQ[#[[1]], #[[2]]] &][[1, 2]], {n, 21}] (* T. D. Noe, Nov 04 2013 *)

A230963 Values of y such that x^2 + y^2 = 73^n with x and y coprime and 0 < x < y.

Original entry on oeis.org

8, 55, 549, 5280, 44403, 325008, 2685304, 27358559, 241709752, 1870181225, 12766175931, 138963670560, 1291487885997, 10519458225072, 74032715923371, 690521409218881, 6773980286782088, 57975621715535095, 433109386513469096, 3345582274543898400
Offset: 1

Views

Author

Colin Barker, Nov 02 2013

Keywords

Comments

The corresponding x-values are in A230962.

Examples

			a(3)=549 because 296^2 + 549^2 = 389017 = 73^3.
		

Crossrefs

Programs

  • Maple
    f:=n ->  max([abs@Re,abs@Im]((3+8*I)^n)):
    map(f, [$1..50]); # Robert Israel, Mar 31 2017
  • Mathematica
    Table[Max[Abs[Re[(3 + 8I)^n]], Abs[Im[(3 + 8I)^n]]], {n, 30}] (* Indranil Ghosh, Mar 31 2017, after formula by Robert Israel *)
  • Python
    from sympy import I, re, im
    print([max(abs(re((3 + 8*I)**n)), abs(im((3 + 8*I)**n))) for n in range(1, 31)]) # Indranil Ghosh, Mar 31 2017, after formula by Robert Israel

Formula

From Robert Israel, Mar 31 2017: (Start)
a(n) = max(abs(Re((3+8i)^n)), abs(Im((3+8i)^n))).
a(n) = abs(Im(3+8i)^n) if and only if 1/4 < frac(n*arctan(8/3)/Pi) < 3/4.(End)
Showing 1-3 of 3 results.