cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A157290 Decimal expansion of 105/Pi^4.

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%I A157290 #22 Jul 01 2024 19:21:30
%S A157290 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,
%T A157290 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,
%U A157290 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
%N A157290 Decimal expansion of 105/Pi^4.
%C A157290 The Product_{p = primes = A000040} (1+1/p^4), the quartic analog to A082020.
%D A157290 Calvin C. Clawson, Mathematical Mysteries: The Beauty and Magic of Numbers, Springer, 2013. See p. 230.
%H A157290 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A157290 Equals A013662/A013666 = Product_{i>=1} (1+1/A030514(i)).
%F A157290 Equals Sum_{k>=1} 1/A005117(k)^4 = 1 + Sum_{k>=1} 1/A113849(k). - _Amiram Eldar_, May 22 2020
%F A157290 Equals 1/A347329. - _Hugo Pfoertner_, Jul 01 2024
%e A157290 1.077928136741855194... = (1+1/2^4)*(1+1/3^4)*(1+1/5^4)*(1+1/7^4)*...
%p A157290 evalf(105/Pi^4) ;
%t A157290 RealDigits[105/\[Pi]^4,10,150][[1]]  (* _Harvey P. Dale_, Mar 20 2011 *)
%o A157290 (PARI) 105/Pi^4 \\ _Charles R Greathouse IV_, Sep 30 2022
%Y A157290 Cf. A005117, A013662, A013666, A030514, A082020, A113849, A347329.
%K A157290 cons,easy,nonn
%O A157290 1,3
%A A157290 _R. J. Mathar_, Feb 26 2009