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 A012885 Suffixes of 357686312646216567629137 (all primes). 3

%I

%S 7,37,137,9137,29137,629137,7629137,67629137,567629137,6567629137,

%T 16567629137,216567629137,6216567629137,46216567629137,

%U 646216567629137,2646216567629137,12646216567629137,312646216567629137,6312646216567629137,86312646216567629137

%N Suffixes of 357686312646216567629137 (all primes).

%C From _Mikk Heidemaa_, Mar 23 2015: (Start)

%C a(2),...,a(24) all have a single representation (in positive integers) as the sum of two squares (e.g., a(24) = 416865370156^2 + 428846797599^2) and as the hypotenuse of a primitive Pythagorean triple (357686312646216567629137^2 = 10132838975618776700465^2 + 357542758042644694110888^2).

%C ---

%C a^2 + b^2 + c^2 + d^2 + e^2 + f^2 = 357686312646216567629137^2;

%C a=304233682432674451033719; b=185074861663432734470527;

%C c=4189176178164916432878; d=33333333333333333333333; e=3333333; f=3.

%C ---

%C a^2 + b^2 + c^2 + d^2 + e^2 + f^2 = 357686312646216567629137^3;

%C a=210197737649788368191109924028342434;

%C b=39738123500625252940689952285037741;

%C c=777777777777777777777777;

%C d=777777777777777777777777;

%C e=777777777777777777;

%C f=777777777777.

%C a=170350493188466620042802284807886346;

%C b=129394423538599186274382140531063939;

%C c=777777777777777777777777;

%C d=777777777777777777777777;

%C e=777777777777777777;

%C f=777777777777.

%C ---

%C x^2 + y^2 = 357686312646216567629137^3;

%C x=144701758632763782416276428525674993;

%C y=157555096461604743754426503960480452;

%C x=149107037120999813337660002835835372;

%C y=153392629723324670471173010334042063.

%C (End)

%H Mikk Heidemaa, <a href="/A012885/b012885.txt">Table of n, a(n) for n = 1..24</a>

%F a(n) = 357686312646216567629137 mod 10^n. - _José de Jesús Camacho Medina_, Dec 21 2016

%e .......................7

%e ......................37

%e .....................137

%e ....................9137

%e ...................29137

%e ..................629137

%e .................7629137

%e ................67629137

%e ...............567629137

%e ..............6567629137

%e .............16567629137

%e ............216567629137

%e ...........6216567629137

%e ..........46216567629137

%e .........646216567629137

%e ........2646216567629137

%e .......12646216567629137

%e ......312646216567629137

%e .....6312646216567629137

%e ....86312646216567629137

%e ...686312646216567629137

%e ..7686312646216567629137

%e .57686312646216567629137

%e 357686312646216567629137

%e ------------------------

%t Table[Mod[357686312646216567629137,10^n] ,{n, 1, 24}] (* _José de Jesús Camacho Medina_, Dec 21 2016 *)

%Y Cf. A024785.

%K nonn,fini

%O 1,1

%A Larry Calmer (larry(AT)wri.com), _Simon Plouffe_

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