OFFSET
1,4
LINKS
David Consiglio, Jr., Table of n, a(n) for n = 1..1000
EXAMPLE
For n=1, 1/1 = 1 matches the first digit of phi (1.618033), so a(1) = 1
For n=2, 2/1 = 2 which matches no digits of phi (1.618033), so a(2) = 0
For n=12,
F(13)/F(12) = 1.6180 55... = 233/144
phi = 1.6180 33...
^ ^^^^ a(12) = 5 matching digits
PROG
(Python)
from math import isqrt
fib = [1, 1]
terms = []
while len(terms) < 1000:
deg = 0
target = 0
test = 0
while target == test:
target = (10**deg+isqrt(5*10**(2*deg)))//2
test = (10**deg*(fib[-1]))//fib[-2]
deg += 1
terms.append(deg-1)
fib.append(fib[-1]+fib[-2])
print(terms)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
David Consiglio, Jr., Jan 31 2024
STATUS
approved