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%I #8 Sep 17 2024 16:23:12
%S 5,11,17,21,23,27,28,29,30,34,36,42,45,48,49,50,52,54,59,60,61,67,70,
%T 72,73,74,78,79,80,83,85,88,91,92,96,98,101,104,105,110,111,115,116,
%U 118,122,123,126,127,129,130,131,132,135,136,141,143,147,152,153,154,155
%N Impossible numbers of trailing zeros in the decimal representation of a factorial of any prime.
%C No entry of A039716 ends with 5, 11, 17, 21,... consecutive zeros.
%t f[n_] := IntegerExponent[Prime@n!, 10]; Complement[ Range[0, 157], Array[f, 115]] (* _Robert G. Wilson v_, Nov 05 2010 *)
%t 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 *)
%Y Cf. A000966.
%K base,nonn
%O 1,1
%A _Lekraj Beedassy_, Oct 31 2010
%E Definition rephrased, keyword:base added by _R. J. Mathar_, Nov 03 2010
%E More terms from _Robert G. Wilson v_, Nov 05 2010