A368549 - OEIS

%I #6 Dec 30 2023 23:19:00

%S 8,12,24,24,20,18,38,14,54,30,138,98,152,90,84,80,240,504,68,200,354,

%T 854,224,1020,230,180,510,542,524,522,368,968,578,1098,1130,3462,744,

%U 504,1218,1988,468,938,812,758,684,4002,2592,642,3120,4458,2958,3272,4920,572,5060,3300,14490,3188,6012

%N a(n) is the least k such that the greatest prime less than n*k is less than n times the greatest prime < k.

%C a(n) = p + 1 where p is the first prime such that there are no primes between n*p and n*(p+1).

%H Robert Israel, <a href="/A368549/b368549.txt">Table of n, a(n) for n = 2..280</a>

%e a(4) = 24 because the greatest prime < 24 is 23 and the greatest prime < 4*24 is 89 < 4*23.

%p f:= proc(n) local p;

%p    p:= 1;

%p    do

%p      p:= nextprime(p);

%p      if not ormap(isprime, [$ (n*p+1) .. (n*p+n-1)]) then return p+1 fi

%p    od

%p end proc:

%p map(f, [$2..100]);

%Y Cf. A367035.

%K nonn

%O 2,1

%A _Robert Israel_, Dec 29 2023