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A068857
a(0) = 0, a(1) = 8; for n>=2: a(n) = smallest multiple of a(n-1) which is of the form 2k*(2k+2).
3
0, 8, 24, 48, 288, 16128, 11950848, 4636929024, 88106288385024, 8038489644431643930624, 15177535939786079616000991061008232448, 40096515501441989312471498490435884509054125751527350190658560000
OFFSET
0,2
LINKS
FORMULA
a(n) = 8 * A068776(n-1) for n>=1.
EXAMPLE
24 = 4*6 is a member and the smallest multiple of 24 which is of the form 2k(2k+2) is 48 = 6*8.
MATHEMATICA
m = 0; {0} ~Join~ Rest@ NestList[(m++; While[! Divisible[Set[k, # (# + 2) &[2 m]], #], m++]; k) &, 1, 8] (* Michael De Vlieger, Mar 18 2024 *)
PROG
(Python)
from itertools import islice
from sympy import sqrt_mod_iter
def A068857_gen(): # generator of terms
yield 0
a = 8
while True:
yield a
b = a+1
for d in sqrt_mod_iter(1, a):
if d==1 or d**2-1 == a:
d += a
if d&1 and d < b:
b = d
a = b**2-1
A068857_list = list(islice(A068857_gen(), 11)) # Chai Wah Wu, May 05 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Mar 12 2002
EXTENSIONS
More terms from Sascha Kurz, Mar 23 2002
a(8) onward corrected by Sean A. Irvine, Mar 18 2024
a(10)-a(11) from Alois P. Heinz, Mar 19 2024
STATUS
approved