A053674 Least number coprime to n, n+1, n+2, n+3, n+4 and n+5.

7, 11, 11, 11, 11, 13, 13, 7, 17, 17, 17, 11, 11, 11, 7, 11, 13, 13, 13, 13, 17, 7, 11, 11, 11, 11, 11, 13, 7, 13, 13, 13, 13, 11, 11, 7, 11, 11, 17, 13, 13, 13, 7, 13, 11, 11, 11, 11, 11, 7, 19, 17, 13, 13, 13, 11, 7, 11, 11, 11, 17, 17, 19, 7, 19, 13, 11, 11, 11, 11, 7, 13

Offset: 1

Author

Henry Bottomley, Feb 15 2000

Keywords

• nonn
• easy
• nice

Comments

All terms are primes greater than 5. Records: a(1) = 7, a(2) = 11, a(6) = 13, a(9) = 17, a(51) = 19, a(151) = 23, a(437) = 29, a(779) = 31, a(1766) = 37, a(60605) = 41, a(324596) = 43, a(3555107) = 47, a(14511250) = 53, a(65209022) = 59, a(764050703) = 61, .... - Charles R Greathouse IV, Feb 07 2017

Links

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

Crossrefs

Cf. A053669-A053673.

Programs

Haskell

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a053674 n = 2 + fromJust
   (elemIndex 1 $ map (gcd $ foldl1 lcm $ take 6 [n..]) [2..])
-- Reinhard Zumkeller, Sep 25 2011

Mathematica

a[n_] := (k = 7; While[ ! And @@ (CoprimeQ[k, #] & ) /@ Range[n, n+5], k++]; k); Table[a[n], {n, 1, 72}] (* Jean-François Alcover, Nov 30 2011 *)
cpr[n_]:=Module[{k=7},While[Union[Boole[CoprimeQ[k,n+Range[0,5]]]]!={1},k = NextPrime[ k]];k](* Harvey P. Dale, May 12 2022 *)

PARI

a(n)=my(L=lcm([n..n+5])); forprime(p=7,, if(L%p, return(p))) \\ Charles R Greathouse IV, Feb 07 2017

Extensions

More terms from Andrew Gacek (andrew(AT)dgi.net), Feb 21 2000 and James Sellers, Feb 22 2000