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A045561
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Numbers whose factorial has '52' as its final two digits before the trailing zeros.
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1
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34, 36, 41, 86, 93, 122, 132, 150, 151, 167, 177, 183, 194, 249, 257, 342, 349, 374, 399, 421, 440, 479, 511, 515, 522, 557, 571, 580, 606, 631, 665, 678, 687, 692, 734, 738, 741, 754, 778, 867, 895, 898, 912, 924, 931, 939, 950, 951, 962, 975, 976, 1012
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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Select[Range[5, 1100], Take[Flatten[Most[Split[IntegerDigits[#!]]]], -2] == {5, 2}&] (* Harvey P. Dale, Aug 08 2016 *)
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PROG
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(PARI) last(n, k)=if(n*8\9-1<k, n=n!; return(n/10^valuation(n, 10)%10^k)); my(m=Mod(1, 5^k)); for(i=2, n, m*=i/10^valuation(i, 5)); lift(chinese(m, Mod(0, 2^k))) \\ Gives the last k decimal digits of n!.
(PARI) is(n)=my(m=Mod(1, 25)); for(i=2, n, m*=i/10^valuation(i, 5)); m==52 && n>2 \\ Charles R Greathouse IV, Oct 22 2014
(PARI) v=List(); m=Mod(6, 25); for(n=4, 1e6, m*=n/10^valuation(n, 5); if(m==52, listput(v, n); if(#v==100, return(Vec(v))))) \\ Charles R Greathouse IV, Oct 22 2014
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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