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Decimal expansion of 1/65537.
1

%I #11 Feb 16 2025 08:33:21

%S 0,0,0,0,1,5,2,5,8,5,5,6,2,3,5,4,0,9,0,0,5,5,9,9,8,9,0,1,3,8,3,9,5,1,

%T 0,5,0,5,5,1,5,9,6,8,0,7,9,1,0,0,3,5,5,5,2,4,3,6,0,2,8,5,0,2,9,8,3,0,

%U 4,7,7,4,4,0,2,2,4,6,0,5,9,4,7,7,8,5,2,2,0,5,6,2,4,3,0,3,8,2,8,3,7,1,7,5,9

%N Decimal expansion of 1/65537.

%C Periodic sequence of period 65536. Being a Fermat prime > 5, 65537 is a full reptend prime. One full period is given in the table.

%H Rick L. Shepherd, <a href="/A236184/b236184.txt">Table of n, a(n) for n = 0..65535</a>

%H MathWorld, <a href="https://mathworld.wolfram.com/FermatPrime.html">Fermat Prime</a>

%F a(n + 65536) = a(n).

%e 0.000015258556235409005599890138395105055159680791003555243602850298304774...

%t RealDigits[1/65537, 10, 105, -1][[1]] (* _T. D. Noe_, Jan 27 2014 *)

%o (PARI)

%o {default(realprecision, 66000);

%o x = 1/65537; d = 0; for(n = 0, 65535, x = (x-d)*10; d = floor(x);

%o write("b236184.txt", n, " ", d))} \\ _Rick L. Shepherd_, Jan 19 2014 (after similar program by Harry J. Smith)

%Y Cf. A007450 (1/17), A021261 (1/257), A019434, A001913, A048963.

%K nonn,cons,easy,changed

%O 0,6

%A _Rick L. Shepherd_, Jan 19 2014