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 1-5 of 5 results.

A230713 Values of y such that x^2 + y^2 = 37^n with x and y coprime and 0 < x < y.

Original entry on oeis.org

6, 35, 198, 1081, 6121, 42372, 281987, 1816080, 11359441, 69118332, 409120667, 2352069720, 13087371961, 70021883892, 454630639122, 3083813678879, 20184430499034, 128112059869885, 790520789974362, 4746103264506599
Offset: 1

Views

Author

Colin Barker, Oct 28 2013

Keywords

Comments

The corresponding x-values are in A230712.

Examples

			a(3)=198 because 107^2+198^2=50653=37^3.
		

Crossrefs

A230743 Values of x such that x^2 + y^2 = 41^n with x and y coprime and 0 < x < y.

Original entry on oeis.org

4, 9, 115, 720, 2476, 42471, 4765, 1788961, 3780956, 51872200, 310486445, 1142532559, 18483128564, 4205436520, 799862636324, 1584162310079, 23384002313285, 133802323596440, 526151093402156, 8041209044472401, 2783579583540395, 357525366658772391
Offset: 1

Views

Author

Colin Barker, Oct 29 2013

Keywords

Comments

The corresponding y-values are in A230744.

Examples

			a(3)=115 because 115^2+236^2=68921=41^3.
		

Crossrefs

Programs

  • Mathematica
    Table[Select[PowersRepresentations[41^n, 2, 2], CoprimeQ@@#&][[1, 1]], {n, 1, 40}] (* Vincenzo Librandi, Mar 02 2014 *)

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 *)

A230841 Values of x such that x^2 + y^2 = 61^n with x and y coprime and 0 < x < y.

Original entry on oeis.org

5, 11, 234, 1320, 9475, 117469, 266286, 9184560, 3302155, 520632300, 1387108806, 23922442439, 154165737965, 933420304380, 13338456688674, 22995028210081, 1026964091673115, 713853567388260, 54078566783400895, 171226928056302601, 2435077776719657394
Offset: 1

Views

Author

Colin Barker, Oct 31 2013

Keywords

Comments

The corresponding y-values are in A230842.

Examples

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

Crossrefs

Programs

  • Mathematica
    Table[Select[PowersRepresentations[61^n, 2, 2], CoprimeQ[#[[1]], #[[2]]] &][[1, 1]], {n, 22}] (* T. D. Noe, Nov 04 2013 *)
    Table[Select[PowersRepresentations[61^n, 2, 2], CoprimeQ@@#&][[1, 1]], {n, 1, 40}] (* Vincenzo Librandi, Mar 02 2014 *)

Extensions

a(10) and a(20) corrected by Zak Seidov, Nov 02 2013

A230962 Values of x such that x^2 + y^2 = 73^n with x and y coprime and 0 < x < y.

Original entry on oeis.org

3, 48, 296, 721, 10072, 213785, 1958709, 7613760, 21165597, 894454032, 12278087704, 59926173839, 62518379032, 3374316625735, 58552907681096, 416603004343680, 1261259807092797, 10231862403603888, 255781764375436389, 2697529798981443601, 11543491568219853608
Offset: 1

Views

Author

Colin Barker, Nov 02 2013

Keywords

Comments

The corresponding y-values are in A230963.

Examples

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

Crossrefs

Programs

  • Maple
    f:=n ->  min([abs@Re,abs@Im]((3+8*I)^n)):
    map(f, [$1..50]); # Robert Israel, Mar 31 2017
  • Mathematica
    Table[Select[PowersRepresentations[73^n, 2, 2], CoprimeQ@@#&][[1, 1]], {n, 1, 40}] (* Vincenzo Librandi, Mar 02 2014 *)
    Table[Min[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([min(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) = min(abs(Re((3+8i)^n)), abs(Im((3+8i)^n))).
a(n) = abs(Re(3+8i)^n) if and only if 1/4 < frac(n*arctan(8/3)/Pi) < 3/4.
(End)
Showing 1-5 of 5 results.