A230744
Values of y such that x^2 + y^2 = 41^n with x and y coprime and 0 < x < y.
Original entry on oeis.org
5, 40, 236, 1519, 10475, 54280, 441284, 2187360, 17694245, 103595049, 673741196, 4610651760, 24155269835, 194708863431, 956722571075, 7826203465920, 45467666569916, 298790677846089, 2029162683616205, 10747406201475600, 85901867185267604, 418375017592176440
Offset: 1
a(3)=236 because 115^2+236^2=68921=41^3.
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
a(3)=259 because 259^2+286^2=148877=53^3.
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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
a(3)=234 because 234^2+415^2=226981=61^3.
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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 *)
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
a(3) = 296 because 296^2 + 549^2 = 389017 = 73^3.
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f:=n -> min([abs@Re,abs@Im]((3+8*I)^n)):
map(f, [$1..50]); # Robert Israel, Mar 31 2017
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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 *)
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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
Showing 1-4 of 4 results.
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