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

Author

Reinhard Zumkeller, Jan 12 2014

Keywords

• nonn

Comments

Nonprimes in A158034.

Links

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

Crossrefs

Cf. A158034, A010051, A002808.

Programs

Haskell

a235540 n = a235540_list !! (n-1)
a235540_list = filter ((== 0) . a010051') a158034_list

Mathematica

Select[Range[10^6],CompositeQ[#]&&IntegerQ[(4^#-2^#+8#^2-2)/(2#(2#+1))]&] (* Harvey P. Dale, Nov 17 2014 *)

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

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