OFFSET
1,1
COMMENTS
In all solutions of this equation n is divisible by 6.
The solution values for n = prime(i) + prime (j), when restricted by the condition prime(i+3) = prime (i) + 2*prime(j). Rather than being overly restrictive, the condition applies to the most prevalent type of solution to the equation above for n^2. See A225461 for details.
The equation is member of an infinite family of similar equations written as: n^2 = prime(i)*prime(i+d) + prime(j)^2, for any i,j, or d > 0. In this instance d = 3.
There are some additional solutions for n that do NOT obey the condition above. These are sparse but include: 60 (a 2nd time), 150, 1434, 4584 and 5190 all of which occur at low values of prime(i) and which obey the condition: n = prime(j) + 1. These are also divisible by 6, but they are excluded from the listing above.
REFERENCES
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
12 is a solution value for N because 12^2 = 7*17 + 5^2 and 17 is the third prime after 7.
PROG
(PARI) is(n)=my(p=2, q=3, r=5, t); forprime(s=7, n+160, if(issquare(n^2-p*s, &t) && isprime(t), return(1)); p=q; q=r; r=s); 0 \\ Charles R Greathouse IV, May 13 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Richard R. Forberg, May 10 2013
STATUS
approved