A359456 - OEIS

%I #40 Dec 15 2024 17:14:49

%S 1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Characteristic function of Fibonorial numbers.

%C Is this constant transcendental? The proof is probably very similar to the proof that Liouville's constant (A012245) is transcendental.

%H Antti Karttunen, <a href="/A359456/b359456.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%e .1100010000000000000000000000010000000000000...

%o (Python)

%o f0, f1, fibonorial = 1, 1, 1

%o for n in range(1,88):

%o     if n == fibonorial:

%o         print("1", end = ", ")

%o         f0, f1 = f0+f1, f0

%o         fibonorial *= f0

%o     else:

%o         print("0", end = ", ")

%o (Python)

%o def A359456(n):

%o     a,b,c = 1,2,1

%o     while (c:=c*a) < n:

%o         a, b = b, a+b

%o     return int(c==n) # _Chai Wah Wu_, Jan 11 2023

%o (PARI) A359456(n) = { my(a=1,b=2,c=1,t); while((c=(c*a))<n, t=a+b; a=b; b=t); (c==n); }; \\ _Antti Karttunen_, Dec 15 2024, after _Chai Wah Wu_

%Y Characteristic function of A003266.

%Y Cf. A012245.

%K nonn,cons,easy

%O 1

%A _A.H.M. Smeets_, Jan 02 2023