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

1,1

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A053669-A053674, A226891.

Sequence in context: A258316 A244621 A201459 * A087525 A078496 A114521

Adjacent sequences: A053669 A053670 A053671 * A053673 A053674 A053675

Keyword

nonn,easy,nice

Author

Henry Bottomley, Feb 15 2000

Extensions

More terms from James A. Sellers, Feb 22 2000

Status

approved