OFFSET
1,1
COMMENTS
This sequence is the sequence of possible c^2 - 1 values of all triples (a,b,c) of integers > 1 such that (a^2 - 1)*(b^2 - 1) = c^2 - 1.
LINKS
David A. Corneth, Table of n, a(n) for n = 1..19120 (first 408 terms from Ely Golden, terms <= 10^17)
David A. Corneth, PARI program
EXAMPLE
120 is a term since 120 = 15*8 = (4^2 - 1)*(3^2 - 1) and 120 = 11^2 - 1.
PROG
(Python)
from math import isqrt
def is_perfect_square(n): return isqrt(abs(n))**2 == n
limit = 10**17
sequence_entries = set()
for a in range(2, isqrt(isqrt(limit))+1):
u = a**2 - 1
for b in range(a+1, isqrt(limit//u+1)+1):
v = b**2 - 1
if(is_perfect_square(u*v + 1)): sequence_entries.add(u*v)
sequence_entries = sorted(sequence_entries)
for i, j in enumerate(sequence_entries, 1):
print(i, j)
(PARI) isok1(k) = issquare(k+1);
isok2(k) = fordiv(k, d, if (isok1(d) && isok1(k/d), return(1)));
isok(k) = isok1(k) && isok2(k); \\ Michel Marcus, May 04 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Ely Golden, May 03 2024
STATUS
approved