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

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, 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, 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

Offset: 1

Author

Henry Bottomley, Feb 15 2000

Keywords

• nonn
• easy
• nice

Comments

From Robert Israel, Jul 06 2016: (Start)

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

All terms are primes >= 7.

First occurrences of the first few values:

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

(End)

Links

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

Crossrefs

Cf. A053669-A053674.

Programs

Haskell

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a053673 n = 2 + fromJust
   (elemIndex 1 $ map (gcd $ foldl1 lcm $ take 5 [n..]) [2..])
-- Reinhard Zumkeller, Sep 25 2011

Maple

f:= proc(n) local p;
  p:= 7;
  while min([n,n+1,n+2,n+3,n+4] mod p) = 0 do p:= nextprime(p) od:
  p
end proc:
seq(f(n),n=1..100); # Robert Israel, Jul 06 2016

Mathematica

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

Extensions

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