A093074 Greatest prime factor of n and its direct neighbors.

2, 3, 3, 5, 5, 7, 7, 7, 5, 11, 11, 13, 13, 13, 7, 17, 17, 19, 19, 19, 11, 23, 23, 23, 13, 13, 13, 29, 29, 31, 31, 31, 17, 17, 17, 37, 37, 37, 19, 41, 41, 43, 43, 43, 23, 47, 47, 47, 7, 17, 17, 53, 53, 53, 11, 19, 29, 59, 59, 61, 61, 61, 31, 13, 13, 67, 67, 67, 23, 71, 71, 73

Offset: 1

Author

Reinhard Zumkeller, Mar 18 2004

Keywords

• nonn

Comments

a(n) = A006530(n + A093075(n));

a(n) = max{A006530(n-1), A006530(n), A006530(n+1)}, n>1;

a(n) = A006530(A007531(n+1)), n>1;

for all primes p>2: a(p)=a(p-1)=p and if p is not the lesser member of a twin prime pair, then also a(p+1)=p;

(n,n+2) is a twin prime pair iff a(n-1)=a(n)=n and a(n+1)=a(n+2)=a(n+3)=n+2.

Links

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

Crossrefs

Cf. A074399, A190136.

Programs

Haskell

a093074 1 = 2
a093074 n = maximum $ map a006530 [n-1..n+1]
-- Reinhard Zumkeller, Jul 04 2012

PARI

a(n)=my(p=precprime(n+1));if(p>n-2,p,vecmax(apply(n->vecmax(factor(n)[,1]),[n-1,n,n+1]))) \\ Charles R Greathouse IV, Feb 19 2013

Formula

a(n) > 47 if n > 212381. - Charles R Greathouse IV, Feb 19 2013