A053673 - OEIS

%I #18 Jul 06 2016 23:47:04

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

%C From _Robert Israel_, Jul 06 2016: (Start)

%C Least prime that does not divide n(n+1)(n+2)(n+3)(n+4).

%C All terms are primes >= 7.

%C First occurrences of the first few values:

%C   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 (End)

%H Reinhard Zumkeller, <a href="/A053673/b053673.txt">Table of n, a(n) for n = 1..10000</a>

%p f:= proc(n) local p;

%p   p:= 7;

%p   while min([n,n+1,n+2,n+3,n+4] mod p) = 0 do p:= nextprime(p) od:

%p   p

%p end proc:

%p seq(f(n),n=1..100); # _Robert Israel_, Jul 06 2016

%t Table[k=2;While[First[Union[CoprimeQ[k,#]&/@(n+Range[0,4])]]== False, k++];k,{n,80}] (* _Harvey P. Dale_, Jul 07 2011 *)

%o (Haskell)

%o import Data.List (elemIndex)

%o import Data.Maybe (fromJust)

%o a053673 n = 2 + fromJust

%o    (elemIndex 1 $ map (gcd $ foldl1 lcm $ take 5 [n..]) [2..])

%o -- _Reinhard Zumkeller_, Sep 25 2011

%Y Cf. A053669-A053674.

%K nonn,easy,nice

%O 1,1

%A _Henry Bottomley_, Feb 15 2000

%E More terms from Andrew Gacek (andrew(AT)dgi.net), Feb 21 2000 and _James A. Sellers_, Feb 22 2000