A242834 - OEIS

%I #16 Feb 18 2023 08:09:08

%S 0,0,6,4,0,3,0,56,0,10,0,4,0,14,0,0,0,306,0,380,0,22,0,552,0,26,0,0,0,

%T 6,0,992,0,34,0,0,0,38,0,0,0,1722,0,1892,0,46,0,2256,0,0,0,0,0,2862,0,

%U 8,0,58,0,3540,0,62,0,0,0,0,0,4556,0,0,0,5112,0,74,0,0,0,0,0,6320,0,82,0,6972

%N Least number k such that k*n/(k+n) is prime or 0 if no such k exists.

%C Since the largest k where k*n/(k+n) is an integer is given by n*(n-1), a(n) = 0 is definite.

%H Antti Karttunen, <a href="/A242834/b242834.txt">Table of n, a(n) for n = 1..10080</a>

%e 1*3/(1+3) = 3/4 is not prime. 2*3/(2+3) = 6/5 is not prime. 3*3/(3+3) = 9/6 is not prime. 4*3/(4+3) = 12/7 is not prime. 5*3/(5+3) = 15/8 is not prime. 6*3/(6+3) = 2 is prime. Thus, a(3) = 6.

%o (PARI) a(n)=for(k=1,n*(n-1),s=(k*n)/(k+n);if(floor(s)==s,if(ispseudoprime(s),return(k))))

%o n=1;while(n<100,print(a(n));n+=1)

%o (PARI) A242834(n) = { for(k=1, n*(n-1), if(!((k*n)%(k+n)) && isprime((k*n)/(k+n)), return(k))); (0); }; \\ _Antti Karttunen_, Feb 18 2023

%Y Cf. A002378, A242931.

%K nonn

%O 1,3

%A _Derek Orr_, May 27 2014

%E Missing terms a(35) .. a(38) inserted by _Antti Karttunen_, Feb 18 2023