OFFSET
1,2
COMMENTS
a(1) = 0; for n>1, a(n) = smallest integer > a(n-1) such that GCD(a(n),a(i))+1 is square for all 1 <= i <= n-1.
EXAMPLE
After a(1)=0, a(2)=3, a(3)=15, we want m, the smallest number > 15 such that GCD(0,m)+1, GCD(3,m)+1 and GCD(15,m)+1 are squares: this is m = 24 = a(4).
PROG
(Sage)
seq = []
prev_element = 0
seq.append( prev_element )
max_n = 35
for n in range(2, max_n+1):
next_element = prev_element + 1
while True:
all_match = True
for element in seq:
x = gcd( element, next_element ) + 1
if not ( is_square(x) ):
all_match = False
break
if all_match:
seq.append( next_element )
print(seq)
break
next_element = next_element + 1
prev_element = next_element
print(seq)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert C. Lyons, Jul 05 2016
STATUS
approved