A157290 Decimal expansion of 105/Pi^4.

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

Offset: 1

Author

R. J. Mathar, Feb 26 2009

Keywords

• cons
• easy
• nonn

Comments

The Product_{p = primes = A000040} (1+1/p^4), the quartic analog to A082020.

Examples

			1.077928136741855194... = (1+1/2^4)*(1+1/3^4)*(1+1/5^4)*(1+1/7^4)*...
		

References

• Calvin C. Clawson, Mathematical Mysteries: The Beauty and Magic of Numbers, Springer, 2013. See p. 230.

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A005117, A013662, A013666, A030514, A082020, A113849, A347329.

Programs

Maple

evalf(105/Pi^4) ;

Mathematica

RealDigits[105/\[Pi]^4,10,150][[1]]  (* Harvey P. Dale, Mar 20 2011 *)

PARI

105/Pi^4 \\ Charles R Greathouse IV, Sep 30 2022

Formula

Equals A013662/A013666 = Product_{i>=1} (1+1/A030514(i)).

Equals Sum_{k>=1} 1/A005117(k)^4 = 1 + Sum_{k>=1} 1/A113849(k). - Amiram Eldar, May 22 2020

Equals 1/A347329. - Hugo Pfoertner, Jul 01 2024