A242834 Least number k such that k*n/(k+n) is prime or 0 if no such k exists.

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, 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, 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

Offset

1,3

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..10080

Example

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.

Prog

(PARI) a(n)=for(k=1, n*(n-1), s=(k*n)/(k+n); if(floor(s)==s, if(ispseudoprime(s), return(k))))
n=1; while(n<100, print(a(n)); n+=1)
(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

Crossrefs

Cf. A002378, A242931.

Sequence in context: A136133 A200020 A011487 * A010495 A111310 A190575

Adjacent sequences: A242831 A242832 A242833 * A242835 A242836 A242837

Keyword

nonn

Author

Derek Orr, May 27 2014

Extensions

Missing terms a(35) .. a(38) inserted by Antti Karttunen, Feb 18 2023

Status

approved