A136801 Largest prime factor of the composites in the n-th prime gap larger than 2.

5, 7, 11, 13, 17, 19, 23, 17, 29, 31, 23, 37, 41, 43, 47, 11, 53, 37, 61, 43, 67, 73, 31, 79, 83, 43, 89, 61, 97, 103, 109, 113, 29, 79, 83, 127, 131, 89, 137, 139, 97, 151, 103, 157, 163, 167, 173, 13, 179, 181, 53, 47, 191, 193, 197, 199, 101, 139, 211, 109, 17, 223

Offset: 1

Author

Enoch Haga, Jan 24 2008

Keywords

• easy
• nonn

Comments

The largest prime factor of numbers in the interval [A136798(n),A136799(n)].

The sequence is obtained from A052248 by removing terms from composites in prime gaps of size 2.

Examples

			a(1)=5 because the composites in the run from 8, 9, 10 contain prime factors 2, 3, and 5, with 5 being the largest at N=10.
		

Crossrefs

Cf. A136798, A136799, A136800, A136802.

Programs

Maple

A006530 := proc(n) max( op(numtheory[factorset](n))) ; end:
A136798 := proc(n) local a; if n = 1 then 8; else a := nextprime( procname(n-1))+1 ; while nextprime(a)-a <=2 do a := nextprime(a)+1 ; od; RETURN(a) ; fi; end:
A136801 := proc(n) local a,i; i := A136798(n) ; a := A006530( i) ; while not isprime(i+1) do i := i+1 ; a := max(a, A006530(i)) ; od: a ; end:
seq(A136801(n),n=1..20) ; # R. J. Mathar, May 27 2009

Extensions

Edited by R. J. Mathar, May 27 2009