%I #6 Sep 21 2015 01:22:36

%S 10,14,22,26,34,38,46,51,58,62,69,74,82,86,94,99,106,111,122,129,134,

%T 146,155,158,166,172,178,183,194,206,218,226,232,237,249,254,262,267,

%U 274,278,291,302,309,314,326,334,346,351,358,362,371,376,382,386,394

%N The composite with the largest prime factor in the n-th prime gap larger than 2.

%C Pick the number in the interval [A136798(n),A136799(n)] with the largest prime factor.

%C The sequence is obtained from A114331 by removing terms in prime gaps of size 2.

%F A006530(a(n)) = A136801(n).

%e a(1)=10 because at N=10 the largest prime factor is 5.

%p A006530 := proc(n) max( op(numtheory[factorset](n))) ; end:

%p 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:

%p A136802 := proc(n) local c,lpf,a; c := A136798(n) ; lpf := A006530(c) ; a := c; while not isprime(c+1) do c := c+1 ; if A006530(c) > lpf then a := c ; lpf := A006530(c) ; fi; od: a ; end:

%p seq(A136802(n),n=1..80) ; # _R. J. Mathar_, May 27 2009

%Y Cf. A136798, A136799, A136800, A136801.

%K easy,nonn

%O 1,1

%A _Enoch Haga_, Jan 24 2008

%E Edited by _R. J. Mathar_, May 27 2009