A374581 - OEIS

%I #19 Jul 15 2024 10:22:44

%S 15,819,19635,15225,69597,466785,911547,179645,533715,4165161,2072385,

%T 8947437,12491175,1133055,22621131,29539125,4214903,48002745,11990775,

%U 24669567,90400695,109375617,43730505,6244749,184439871,24049985,252455907,292777485,22516425,387706641

%N a(n) is the denominator of (120*n^2 + 151*n + 47)/(512*n^4 + 1024*n^3 + 712*n^2 + 194*n + 15).

%C See Bailey and Crandall (2001), section 5 (pp. 183-184) for a derivation of this rational polynomial.

%C Numerators are given by A374580.

%H Paolo Xausa, <a href="/A374581/b374581.txt">Table of n, a(n) for n = 0..10000</a>

%H David H. Bailey and Richard E. Crandall, <a href="https://doi.org/10.1080/10586458.2001.10504441">On the Random Character of Fundamental Constant Expansions</a>, Experimental Mathematics, Vol. 10 (2001), Issue 2, pp. 175-190 (<a href="https://www.davidhbailey.com/dhbpapers/baicran.pdf">preprint draft</a>).

%F Sum_{n >= 0} (1/16^n)*A374580(n)/a(n) = A000796. See Bailey and Crandall (2001), eq. 5-2, p. 184.

%t A374581[n_] := Denominator[(120*n^2 + 151*n + 47)/(512*n^4 + 1024*n^3 + 712*n^2 + 194*n + 15)];

%t Array[A374581, 30, 0]

%o (Python)

%o from math import gcd

%o def A374581(n): return (lambda p,q: q//gcd(p,q))(n*(120*n + 151) + 47,n*(n*(n*(512*n + 1024) + 712) + 194) + 15) # _Chai Wah Wu_, Jul 14 2024

%Y Cf. A000796, A001025, A374335, A374580 (numerators), A374608.

%K nonn,frac

%O 0,1

%A _Paolo Xausa_, Jul 12 2024