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

Author

Lekraj Beedassy, Oct 31 2010

Keywords

• base
• nonn

Comments

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

Crossrefs

Cf. A000966.

Programs

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 *)

Extensions

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

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