A242931 Largest number k such that k*n/(k+n) is prime or 0 if no such k exists.

0, 0, 6, 12, 0, 30, 0, 56, 0, 10, 0, 132, 0, 182, 0, 0, 0, 306, 0, 380, 0, 22, 0, 552, 0, 26, 0, 0, 0, 870, 0, 992, 0, 34, 0, 0, 0, 1406, 0, 0, 0, 1722, 0, 1892, 0, 46, 0, 2256, 0, 0, 0, 0, 0, 2862, 0, 8, 0, 58, 0, 3540, 0, 3782, 0, 0, 0, 0, 0, 4556, 0, 0, 0, 5112, 0, 5402

Offset

1,3

Comments

Since the largest k that makes k*n/(k+n) an integer is n*(n-1), the zero terms are definite.

Apart from 0's, sequence contains a few duplicates. a(6) = a(870) = 30 is one. - Antti Karttunen, Feb 18 2023

Links

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

Example

(6*3)/(6+3) = 2 is prime. Since 6 = 3*(3-1), 6 is the largest number that makes k*n/(k+n) an integer. Thus a(3) = 6.

Prog

(PARI) a(n)=for(k=n*(1-n), 0, s=(-k*n)/(-k+n); if(floor(s)==s, if(ispseudoprime(s), return(-k))))
n=1; while(n<100, print1(a(n), ", "); n+=1)

Crossrefs

Cf. A242834, A002378.

Sequence in context: A243017 A084342 A243045 * A341828 A110645 A064913

Adjacent sequences: A242928 A242929 A242930 * A242932 A242933 A242934

Keyword

nonn

Author

Derek Orr, May 27 2014

Status

approved