Distribution of 0 digits in factorial series: Difference between revisions
Distribution of 0 digits in factorial series (view source)
Revision as of 09:27, 21 June 2021
, 2 years ago→{{header|Python}}
Line 728:
plt.plot([i+1 for i in range(len(props))], props)
</lang>
=== Base 1000 version ===
{{trans|Go via Phix via Pascal}}
<lang python>def zinit():
zc = [0] * 999
for x in range(1, 10):
zc[x - 1] = 2 # 00x
zc[10 * x - 1] = 2 # 0x0
zc[100 * x - 1] = 2 # x00
for y in range(10, 100, 10):
zc[y + x - 1] = 1 # 0yx
zc[10 * y + x - 1] = 1 # y0x
zc[10 * (y + x) - 1] = 1 # yx0
return zc
def meanfactorialdigits():
zc = zinit()
rfs = [1]
total, trail, first, got_first = 0.0, 1, 0, False
for f in range(2, 50000):
carry, d999, zeroes = 0, 0, (trail - 1) * 3
j, l = trail, len(rfs)
while j <= l or carry != 0:
if j <= l:
carry = rfs[j-1] * f + carry
d999 = carry % 1000
if j <= l:
rfs[j-1] = d999
else:
rfs.append(d999)
zeroes += 3 if d999 == 0 else zc[d999-1]
carry //= 1000
j += 1
while rfs[trail-1] == 0:
trail += 1
# d999 is a quick correction for length and zeros
d999 = rfs[-1]
d999 = 0 if d999 >= 100 else 2 if d999 < 10 else 1
zeroes -= d999
digits = len(rfs) * 3 - d999
total += zeroes / digits
ratio = total / f
if f in [100, 1000, 10000]:
print("The mean proportion of zero digits in factorials to {} is {}".format(f, ratio))
if ratio < 0.16 and not got_first:
got_first = True
first = f
if got_first and ratio >= 0.16:
got_first = False
first = 0
print("The mean proportion dips permanently below 0.16 at {}.".format(first))
import time
TIME0 = time.perf_counter()
meanfactorialdigits()
print("\nTotal time:", time.perf_counter() - TIME0, "seconds.")
</lang>{{out}}
<pre>
The mean proportion of zero digits in factorials to 100 is 0.24675318616743216
The mean proportion of zero digits in factorials to 1000 is 0.20354455110316458
The mean proportion of zero digits in factorials to 10000 is 0.17300384824186707
The mean proportion dips permanently below 0.16 at 47332.
Total time: 648.3583232999999 seconds.
</pre>
=={{header|Raku}}==
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