A181573 Impossible numbers of trailing zeros in the decimal representation of a factorial of any prime.

5, 11, 17, 21, 23, 27, 28, 29, 30, 34, 36, 42, 45, 48, 49, 50, 52, 54, 59, 60, 61, 67, 70, 72, 73, 74, 78, 79, 80, 83, 85, 88, 91, 92, 96, 98, 101, 104, 105, 110, 111, 115, 116, 118, 122, 123, 126, 127, 129, 130, 131, 132, 135, 136, 141, 143, 147, 152, 153, 154, 155

Offset

1,1

Comments

No entry of A039716 ends with 5, 11, 17, 21,... consecutive zeros.

Links

Table of n, a(n) for n=1..61.

Mathematica

f[n_] := IntegerExponent[Prime@n!, 10]; Complement[ Range[0, 157], Array[f, 115]] (* Robert G. Wilson v, Nov 05 2010 *)
zOF[n_Integer?Positive]:=Module[{maxpow=0}, While[5^maxpow<=n, maxpow++]; Plus@@Table[ Quotient[n, 5^i], {i, maxpow-1}]]; Attributes[zOF]={Listable}; With[{z=Union[zOF[Prime[Range[ 150]]]]}, Complement[ Range[Max[z]], z]] (* Harvey P. Dale, Sep 17 2024 *)

Crossrefs

Cf. A000966.

Sequence in context: A314183 A314184 A232010 * A314185 A314186 A314187

Adjacent sequences: A181570 A181571 A181572 * A181574 A181575 A181576

Keyword

base,nonn

Author

Lekraj Beedassy, Oct 31 2010

Extensions

Definition rephrased, keyword:base added by R. J. Mathar, Nov 03 2010

More terms from Robert G. Wilson v, Nov 05 2010

Status

approved