OFFSET
1,2
COMMENTS
m = i^2 + 4*j is a term for i > 0, 0 <= j < i. Proof: If p = 2, then i^2 < 2*p + m < (i+2)^2. Therefore (i+1)^2 = 4 + i^2 + 4*j, which leads to a contradiction. If p > 2 is such that 2*p + i^2 + 4*j = k^2, then k + i and k - i are both even numbers. Therefore 4 | 2*p + 4*j, which is also a contradiction.
FORMULA
Conjecture: for k > 0 and 1 <= j <= k, a(2k^2-2j+1) = 4k^2+4k-4j-3, a(2k^2-2j+2) = 4k^2+4k-4j, a(2k^2+2k-2j+1) = 4k^2+8k-4j, a(2k^2+2k-2j+2) = 4k^2+8k-4j+1. - Jinyuan Wang, Jul 23 2019
PROG
(Python)
a=[]
a.append(0) #Offset starts at 1
iMax=15 #Example value
for i in range(1, iMax+1):
for j in range(0, i):
m=i*i+j*4
a.append(m)
a.sort()
CROSSREFS
KEYWORD
nonn
AUTHOR
Bob Andriesse, May 25 2019
STATUS
approved