%I #14 Oct 01 2022 14:14:09

%S 3,6,9,5,7,5,3,6,1,1,6,8,6,3,6,0,6,6,8,0,9,5,0,0,1,9,7,6,1,6,2,7,2,9,

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

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

%N Decimal expansion of 36/Pi^4.

%C Ernesto Cesaro asserted that lim n -> infinity A002321(n)/n = 36/Pi^4 using a fallacious argument. In fact this limit equals zero.

%D Ernesto Cesaro, Sur diverses questions d'arithmetique. Mem. Soc. Roy. Sci. Liege 10 (1883), 1-350. Reprinted in Opere Scelte I, Vol. 1, pp. 10-362.

%D Wladyslaw Narkiewicz, The development of prime number theory: from Euclid to Hardy and Littlewood, Springer-Verlag, New York, 2000, p. 31.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals Product_{primes p} (1 - 2/p^2 + 1/p^4). - _Vaclav Kotesovec_, Jun 20 2020

%e 36/Pi^4 = 0.369575361168636066809500197....

%t RealDigits[N[36/Pi^4, 105]][[1]]

%o (Magma) pi:=Pi(RealField(107)); Reverse(Intseq(Floor(10^105*36/pi^4)))

%o (PARI) default(realprecision, 105); x=360/Pi^4; for(n=1, 105, d=floor(x); x=(x-d)*10; print1(d, ", "));

%Y Cf. A000796, A002321.

%K nonn,cons,easy

%O 0,1

%A _Arkadiusz Wesolowski_, Oct 09 2013