A227929 Decimal expansion of 36/Pi^4.

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, 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, 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

Offset: 0

Author

Arkadiusz Wesolowski, Oct 09 2013

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			36/Pi^4 = 0.369575361168636066809500197....
		

References

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

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A000796, A002321.

Programs

Magma

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

Mathematica

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

PARI

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

Formula

Equals Product_{primes p} (1 - 2/p^2 + 1/p^4). - Vaclav Kotesovec, Jun 20 2020

Equals 1/A098198. - R. J. Mathar, Jul 21 2025