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A139023
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Smallest prime factor of n! + 2^n - 1.
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7
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2, 5, 13, 3, 151, 3, 5167, 3, 7, 3, 39918847, 3, 17, 3, 7, 3, 829, 3, 25561, 3, 7, 3, 929, 3, 67, 3, 7, 3, 37, 3, 941, 3, 7, 3, 31, 3, 47, 3, 7, 3, 839, 3, 167, 3, 7, 3, 101, 3, 859, 3, 7, 3, 165437, 3, 23, 3, 7, 3, 199, 3, 526588200926847656291, 3, 7, 3, 31, 3, 157, 3, 7, 3
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OFFSET
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1,1
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LINKS
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MAPLE
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# this code will produce FAIL for terms that can't be computed within a
# 30 second time limit
spf:= proc(n) local F;
F:= select(f -> f[1]::integer, ifactors(n, easy)[2]);
if F = [] then F:= traperror(timelimit(30, ifactors(n)[2])) fi;
if F = lasterror then FAIL else min(seq(f[1], f=F)) fi
end proc:
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MATHEMATICA
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a = {}; Do[AppendTo[a, n! + 2^n - 1], {n, 1, 40}]; b = {}; Do[c = FactorInteger[a[[n]]]; d = c[[1]]; AppendTo[b, d[[1]]], {n, 1, Length[a]}]; b
Table[FactorInteger[n! + 2^n - 1] [[1, 1]], {n, 1, 40}] (* Vincenzo Librandi, Sep 18 2016 *)
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PROG
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(Magma) trialdiv:=function(n, P) val:=0; for p in P do if n mod p eq 0 then val:=p; break; end if; end for; return val; end function; P:=PrimesUpTo(300000000); [ trialdiv(a, P) where a is Factorial(n)+2^n-1: n in [1..70] ]; //a(61) requires a separate computation. // Klaus Brockhaus, Nov 06 2009
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(1) - a(40) verified and a(41) - a(70) added by Klaus Brockhaus, Nov 06 2009
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STATUS
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approved
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