A048433 -id:A048433 - cp's OEIS frontend

A048434 Smallest denominator of fraction using palindromes that approximates 'phi' to at least n digits after the decimal point.

3, 131, 131, 343, 48384, 578875, 2686862, 161656161, 344363443, 13666666631, 22113131122, 1596916196951, 3256487846523, 115345262543511, 414720808027414, 15801167176110851, 39249297679294293, 988331239932133889, 988331239932133889

Offset: 1

Patrick De Geest, Apr 15 1999

			n=10: 22113131122/13666666631 = 1.6180339887... which is correct to ten digits after the decimal point.

Numerators in A048433.

Cf. A001622 (phi).

a(1) corrected and a(14)-a(19) from Sean A. Irvine, Jun 17 2021

A369715 Number of digits of phi (the golden ratio) correctly approximated by Fibonacci(n+1) / Fibonacci(n).

Original entry on oeis.org

1, 0, 1, 2, 2, 2, 3, 3, 3, 4, 3, 5, 5, 6, 6, 6, 7, 6, 8, 8, 9, 8, 10, 10, 10, 11, 11, 11, 12, 11, 13, 13, 14, 13, 14, 15, 16, 15, 16, 17, 17, 17, 18, 18, 18, 19, 19, 20, 19, 21, 21, 22, 22, 22, 23, 23, 24, 24, 25, 24, 25, 26, 26, 27, 27, 28, 28, 28, 29, 29, 30, 30, 30

Offset: 1

David Consiglio, Jr., Jan 31 2024

			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

David Consiglio, Jr., Table of n, a(n) for n = 1..1000

Cf. A000045, A001622, A048433, A048434.

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)

cp's OEIS Frontend

A048434 Smallest denominator of fraction using palindromes that approximates 'phi' to at least n digits after the decimal point.

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A369715 Number of digits of phi (the golden ratio) correctly approximated by Fibonacci(n+1) / Fibonacci(n).

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Python