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

1,1

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

Formula

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

Prog

(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

Crossrefs

Cf. A074399, A190136.

Sequence in context: A349338 A074399 A090302 * A284412 A136548 A007917

Adjacent sequences: A093071 A093072 A093073 * A093075 A093076 A093077

Keyword

nonn

Author

Reinhard Zumkeller, Mar 18 2004

Status

approved