A235540 - OEIS

%I #20 Feb 14 2021 18:36:24

%S 243,891,1539,2211,2511,13203,19683,87723,92583,150851,202851,292923,

%T 321651,399771,412623,452051,1325843,1330551,1441091,1566891,3026871,

%U 4422231,4954851,4974971,5016191,5845851,5971239,6773139,11050911,11720511,12602871,14666751

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

%C Nonprimes in A158034.

%H Chai Wah Wu, <a href="/A235540/b235540.txt">Table of n, a(n) for n = 1..89</a>

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

%o (Haskell)

%o a235540 n = a235540_list !! (n-1)

%o a235540_list = filter ((== 0) . a010051') a158034_list

%o (Python)

%o from gmpy2 import is_prime, powmod, t_mod

%o A235540_list = []

%o for i in range(1,10**9+1):

%o ....if not is_prime(i):

%o ........d = 2*i*(2*i+1)

%o ........n = t_mod(powmod(4,i,d)-powmod(2,i,d)+8*i*i-2,d)

%o ........if not n:

%o ............A235540_list.append(i) # _Chai Wah Wu_, Dec 02 2014

%Y Cf. A158034, A010051, A002808.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jan 12 2014

%E New definition from _Reinhard Zumkeller_, Nov 17 2014. Thanks to _Harvey P. Dale_, who observed that the original definition was wrong.

%E More terms from _Harvey P. Dale_, Nov 17 2014

%E More terms from _Chai Wah Wu_, Dec 02 2014