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A053673 Least number > 1 coprime to n, n+1, n+2, n+3 and n+4.

%I A053673 #19 Jul 02 2025 16:01:59
%S A053673 7,7,11,11,11,11,13,7,7,17,17,11,11,11,7,7,11,13,13,13,13,7,7,11,11,
%T A053673 11,11,11,7,7,13,13,13,11,11,7,7,11,11,13,13,13,7,7,11,11,11,11,11,7,
%U A053673 7,17,13,13,13,11,7,7,11,11,11,17,17,7,7,13,11,11,11,11,7,7,13,17,17,17,17
%N A053673 Least number > 1 coprime to n, n+1, n+2, n+3 and n+4.
%C A053673 From _Robert Israel_, Jul 06 2016: (Start)
%C A053673 Least prime that does not divide n(n+1)(n+2)(n+3)(n+4).
%C A053673 All terms are primes >= 7.
%C A053673 First occurrences of the first few values:
%C A053673   a(1) = 7, a(3) = 11, a(7) = 13, a(10) = 17, a(117) = 19, a(152) = 23, a(1309) = 29, a(986) = 31, a(1767) = 37, a(203201) = 41, a(868868) = 43
%C A053673 (End)
%H A053673 Reinhard Zumkeller, <a href="/A053673/b053673.txt">Table of n, a(n) for n = 1..10000</a>
%p A053673 f:= proc(n) local p;
%p A053673   p:= 7;
%p A053673   while min([n,n+1,n+2,n+3,n+4] mod p) = 0 do p:= nextprime(p) od:
%p A053673   p
%p A053673 end proc:
%p A053673 seq(f(n),n=1..100); # _Robert Israel_, Jul 06 2016
%t A053673 Table[k=2;While[First[Union[CoprimeQ[k,#]&/@(n+Range[0,4])]]== False, k++];k,{n,80}] (* _Harvey P. Dale_, Jul 07 2011 *)
%o A053673 (Haskell)
%o A053673 import Data.List (elemIndex)
%o A053673 import Data.Maybe (fromJust)
%o A053673 a053673 n = 2 + fromJust
%o A053673    (elemIndex 1 $ map (gcd $ foldl1 lcm $ take 5 [n..]) [2..])
%o A053673 -- _Reinhard Zumkeller_, Sep 25 2011
%Y A053673 Cf. A053669-A053674.
%K A053673 nonn,easy,nice
%O A053673 1,1
%A A053673 _Henry Bottomley_, Feb 15 2000
%E A053673 More terms from Andrew Gacek (andrew(AT)dgi.net), Feb 21 2000 and _James Sellers_, Feb 22 2000