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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.

%I A235540 #22 May 22 2025 10:21:36
%S A235540 243,891,1539,2211,2511,13203,19683,87723,92583,150851,202851,292923,
%T A235540 321651,399771,412623,452051,1325843,1330551,1441091,1566891,3026871,
%U A235540 4422231,4954851,4974971,5016191,5845851,5971239,6773139,11050911,11720511,12602871,14666751
%N A235540 Composite numbers m such that (4^m - 2^m + 8*m^2 - 2) / (2*m*(2*m + 1)) is an integer.
%C A235540 Nonprimes in A158034.
%H A235540 Chai Wah Wu, <a href="/A235540/b235540.txt">Table of n, a(n) for n = 1..89</a>
%t A235540 Select[Range[10^6],CompositeQ[#]&&IntegerQ[(4^#-2^#+8#^2-2)/(2#(2#+1))]&] (* _Harvey P. Dale_, Nov 17 2014 *)
%o A235540 (Haskell)
%o A235540 a235540 n = a235540_list !! (n-1)
%o A235540 a235540_list = filter ((== 0) . a010051') a158034_list
%o A235540 (Python)
%o A235540 from gmpy2 import is_prime, powmod, t_mod
%o A235540 A235540_list = []
%o A235540 for i in range(1,10**9+1):
%o A235540     if not is_prime(i):
%o A235540         d = 2*i*(2*i+1)
%o A235540         n = t_mod(powmod(4,i,d)-powmod(2,i,d)+8*i*i-2,d)
%o A235540         if not n:
%o A235540             A235540_list.append(i) # _Chai Wah Wu_, Dec 02 2014
%Y A235540 Cf. A158034, A010051, A002808.
%K A235540 nonn
%O A235540 1,1
%A A235540 _Reinhard Zumkeller_, Jan 12 2014
%E A235540 New definition from _Reinhard Zumkeller_, Nov 17 2014. Thanks to _Harvey P. Dale_, who observed that the original definition was wrong.
%E A235540 More terms from _Harvey P. Dale_, Nov 17 2014
%E A235540 More terms from _Chai Wah Wu_, Dec 02 2014