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
a(3)=115 because 115^2+236^2=68921=41^3.
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Table[Select[PowersRepresentations[41^n, 2, 2], CoprimeQ@@#&][[1, 1]], {n, 1, 40}] (* Vincenzo Librandi, Mar 02 2014 *)
A230760
Values of y such that x^2 + y^2 = 53^n with x and y coprime and 0 < x < y.
Original entry on oeis.org
7, 45, 286, 2520, 20122, 148148, 1007606, 6254640, 46181513, 391594275, 3034699661, 21731298679, 143399099473, 855828562635, 7344390292954, 60173627260320, 453178096117918, 3155291100853892, 20155636317704834, 131804682060038201, 1152529734625490207
Offset: 1
a(3)=286 because 259^2+286^2=148877=53^3.
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
a(3)=415 because 234^2+415^2=226981=61^3.
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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
a(3)=549 because 296^2 + 549^2 = 389017 = 73^3.
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f:=n -> max([abs@Re,abs@Im]((3+8*I)^n)):
map(f, [$1..50]); # Robert Israel, Mar 31 2017
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Table[Max[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([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
Showing 1-4 of 4 results.
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