A053672 Least number coprime to n, n+1, n+2 and n+3.

5, 7, 7, 11, 11, 5, 11, 7, 7, 7, 5, 11, 11, 11, 7, 5, 7, 11, 13, 13, 5, 7, 7, 7, 11, 5, 11, 11, 7, 7, 5, 13, 13, 11, 11, 5, 7, 7, 11, 11, 5, 13, 7, 7, 7, 5, 11, 11, 11, 7, 5, 7, 13, 13, 13, 5, 7, 7, 7, 11, 5, 11, 17, 7, 7, 5, 11, 11, 11, 11, 5, 7, 7, 13, 17, 5, 17, 7, 7, 7, 5, 11, 11, 11, 7

Offset: 1

Author

Henry Bottomley, Feb 15 2000

Keywords

• nonn
• easy
• nice

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A053669-A053674, A226891.

Programs

Haskell

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a053672 n = 2 + fromJust
   (elemIndex 1 $ map (gcd $ foldl1 lcm $ take 4 [n..]) [2..])
-- Reinhard Zumkeller, Sep 25 2011

Mathematica

a[n_] := (k = 5; While[ ! (CoprimeQ[k, n] && CoprimeQ[k, n+1] && CoprimeQ[k, n+2] && CoprimeQ[k, n+3]), k++]; k); Table[a[n], {n, 1, 85}](* Jean-François Alcover, Nov 30 2011 *)
Table[Module[{k=3},While[!And@@CoprimeQ[n+Range[0,3],Prime[k]],k++];Prime[k]],{n,90}] (* Harvey P. Dale, May 10 2012 *)

PARI

a(n)=forprime(p=5,,if((n+3)%p>3,return(p))) \\ Charles R Greathouse IV, Jun 20 2013

Formula

5 <= a(n) <= (4 + o(1)) log n. - Charles R Greathouse IV, Jun 20 2013

Extensions

More terms from James Sellers, Feb 22 2000