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A235540
Composite numbers m such that (4^m - 2^m + 8*m^2 - 2) / (2*m*(2*m + 1)) is an integer.
3
243, 891, 1539, 2211, 2511, 13203, 19683, 87723, 92583, 150851, 202851, 292923, 321651, 399771, 412623, 452051, 1325843, 1330551, 1441091, 1566891, 3026871, 4422231, 4954851, 4974971, 5016191, 5845851, 5971239, 6773139, 11050911, 11720511, 12602871, 14666751
OFFSET
1,1
COMMENTS
Nonprimes in A158034.
LINKS
MATHEMATICA
Select[Range[10^6], CompositeQ[#]&&IntegerQ[(4^#-2^#+8#^2-2)/(2#(2#+1))]&] (* Harvey P. Dale, Nov 17 2014 *)
PROG
(Haskell)
a235540 n = a235540_list !! (n-1)
a235540_list = filter ((== 0) . a010051') a158034_list
(Python)
from gmpy2 import is_prime, powmod, t_mod
A235540_list = []
for i in range(1, 10**9+1):
....if not is_prime(i):
........d = 2*i*(2*i+1)
........n = t_mod(powmod(4, i, d)-powmod(2, i, d)+8*i*i-2, d)
........if not n:
............A235540_list.append(i) # Chai Wah Wu, Dec 02 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jan 12 2014
EXTENSIONS
New definition from Reinhard Zumkeller, Nov 17 2014. Thanks to Harvey P. Dale, who observed that the original definition was wrong.
More terms from Harvey P. Dale, Nov 17 2014
More terms from Chai Wah Wu, Dec 02 2014
STATUS
approved