A058376 Where the race of the count of final nonzero digit of k! changes, starting at k=2.

2, 16, 50, 80, 88, 108, 110, 264, 273, 291, 326, 336, 669, 671, 678, 685, 718, 721, 738, 764, 773, 791, 826, 836, 1433, 1435, 1558, 1560, 1616, 1629, 1636, 1694, 1696, 1764, 1773, 1791, 1826, 1836, 1928, 1935, 1968, 1971, 1988, 2014, 2023, 2041, 2076, 2086

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Index entries for sequences related to final digits of numbers

Example

a(1) = 2 to start the race. At 15! the number of final twos is 5 and so is the number of eights. But at 16, eights now lead twos, so a(2) = 16 to reflect this fact.
When k=10000 is reached, the count stands at 2509 twos, 2486 fours, 2494 sixes, and 2510 eights.

Mathematica

f[ n_Integer, m_Integer ] := (c = 0; p = 1; While[ d = Floor[ n/5^p ]; d > 0, c = c + d; p++ ]; Mod[ n!/10^c, m ]); a = Table[ 0, {4} ]; r = 4; Do[ b = f[ n, 10 ]; Switch[ b, 2, a[ [ 1 ] ]++, 4, a[ [ 2 ] ]++, 6, a[ [ 3 ] ]++, 8, a[ [ 4 ] ]++ ]; If[ a[ [ b/2 ] ] > a[ [ r/2 ] ], r = b; Print[ n ] ], {n, 2, 10^4} ]

Prog

(Python)
from functools import reduce
from itertools import count, islice
from sympy.ntheory.factor_ import digits
def A058376_gen(): # generator of terms
    a, k, i = [0]*4, 0, 1
    for n in count(2):
        m = (reduce(lambda x, y:x*y%10, ((1, 1, 2, 6, 4)[a]*((6, 2, 4, 8)[i*a&3] if i*a else 1) for i, a in enumerate(digits(n, 5)[-1:0:-1])))*6%10>>1)-1
        a[m] += 1
        if a[m] > k:
            if m!=i:
                yield n
            i, k = m, a[m]
A058376_list = list(islice(A058376_gen(), 48)) # Chai Wah Wu, Dec 07 2023

Crossrefs

Cf. A045547, A045548, A045549, A045550.

Sequence in context: A063721 A232209 A012180 * A295906 A120948 A090453

Adjacent sequences: A058373 A058374 A058375 * A058377 A058378 A058379

Keyword

nonn,base

Author

Robert G. Wilson v, Dec 19 2000

Extensions

Offset 1 from Michel Marcus, Jul 25 2021

Status

approved