%I
%S 1,4,6,8,9,10,12,14,15,16,20,21,22,24,25,26,27,30,32,33,34,35,36,38,
%T 39,42,44,45,46,48,49,50,51,52,54,55,56,57,58,62,63,64,65,66,68,69,70,
%U 74,75,76,77,80,81,84,85,86,87,88,90,91,92,93,94,95,98,99,100
%N Numbers n such that nextprime(5*n)<5*nextprime(n) (if p is prime then nextprime(p)=p).
%C denote f(x)=nextprime(x) let A(p)={n/f(p*n)<f(p)*f(n)} and A(q)={n/f(q*n)<f(q)*f(n)} (q,p are prime) if q<p all terms of A(q) are in A(p). if B(p)={n/f(p*n)>f(p)*f(n)} I conjectured that when p > infinity, A(p) = All composite positive integers when p > infinity, B(p) = All primes numbers
%e nextprime(5*4)=23 and nextprime(5)*nextprime(4)=5*5=25 then 4 is member because 23<15
%o (PARI) for(i=1,100,if(nextprime(5*i)<nextprime(5)*nextprime(i),print1(i,",")))
%K easy,nonn
%O 1,2
%A Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Apr 18 2006
