A374607 - OEIS

%I #23 Jul 15 2024 10:22:49

%S 193,1153,20029,832,111073,50077,327757,7816,724513,251857,1355773,

%T 55511,2275969,715357,3539533,134909,5200897,1549441,7314493,133717,

%U 9934753,2862973,13116109,233347,16912993,4764817,21379837,746297,26571073,7363837,32541133,1119851

%N a(n) is the numerator of (1134*n^3 + 2097*n^2 + 1188*n + 193)/(10368*n^4 + 20736*n^3 + 14112*n^2 + 3744*n + 320).

%C See Bailey and Crandall (2001), section 5 (pp. 183-185) for a derivation of this rational polynomial.

%C Denominators are given by A374608.

%H Paolo Xausa, <a href="/A374607/b374607.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 sqrt(27)*(Sum_{n >= 0} (1/64^n)*a(n)/A374608(n)) = A000796. See Bailey and Crandall (2001), p. 185.

%t A374607[n_] := Numerator[(1134*n^3 + 2097*n^2 + 1188*n + 193)/(10368*n^4 + 20736*n^3 + 14112*n^2 + 3744*n + 320)];

%t Array[A374607, 50, 0]

%o (Python)

%o from math import gcd

%o def A374607(n): return (p:=n*(n*(1134*n + 2097) + 1188) + 193)//gcd(p,n*(n*(n*(324*n + 648) + 441) + 117) + 10<<5) # _Chai Wah Wu_, Jul 14 2024

%Y Cf. A000796, A010482, A089357, A374334, A374580, A374608 (denominators).

%K nonn,frac

%O 0,1

%A _Paolo Xausa_, Jul 13 2024