A235540 Composite numbers m such that (4^m - 2^m + 8*m^2 - 2) / (2*m*(2*m + 1)) is an integer.

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

Chai Wah Wu, Table of n, a(n) for n = 1..89

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

Cf. A158034, A010051, A002808.

Sequence in context: A331613 A255626 A205049 * A219132 A232285 A113335

Adjacent sequences: A235537 A235538 A235539 * A235541 A235542 A235543

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