A276389 Numbers n such that n! ends in the same number of 0's in both base 10 and base 16.

0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 20, 21, 22, 23, 28, 29, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 65, 70, 71, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 90, 91, 95, 100, 101

Offset

1,3

References

Bill Gosper, Posting to Math Fun List, Sep 03 2016

Links

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

Mathematica

esn0Q[n_]:=Module[{z10=Split[IntegerDigits[n!]][[-1]], z16=Split[IntegerDigits[n!, 16]][[-1]]}, MemberQ[z10, 0]&&MemberQ[z16, 0]&&Length[z10]==Length[z16]]; Join[ {0, 1, 2, 3, 4}, Select[Range[0, 120], esn0Q]] (* Harvey P. Dale, Oct 03 2022 *)

Prog

(Python)
A276389_list, m = [0], 1
for n in range(1, 10**3):
    m *= n
    s, h = str(m), hex(m)
    if not len(s)-len(s.rstrip('0'))+len(h.rstrip('0'))-len(h):
        A276389_list.append(n) # Chai Wah Wu, Sep 04 2016

Crossrefs

Sequence in context: A132329 A230313 A052413 * A302058 A183302 A323733

Adjacent sequences: A276386 A276387 A276388 * A276390 A276391 A276392

Keyword

nonn

Author

N. J. A. Sloane, Sep 04 2016

Status

approved