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A296369 Numbers m such that 2^m == -1/2 (mod m).

%I A296369 #22 Aug 27 2021 01:47:21
%S A296369 1,5,65,377,1189,1469,25805,58589,134945,137345,170585,272609,285389,
%T A296369 420209,538733,592409,618449,680705,778805,1163065,1520441,1700945,
%U A296369 2099201,2831009,4020029,4174169,4516109,5059889,5215769
%N A296369 Numbers m such that 2^m == -1/2 (mod m).
%C A296369 Equivalently, 2^(m+1) == -1 (mod m), or m divides 2^(m+1) + 1.
%C A296369 The sequence is infinite, see A055685.
%H A296369 Chai Wah Wu, <a href="/A296369/b296369.txt">Table of n, a(n) for n = 1..1192</a>
%H A296369 OEIS Wiki, <a href="/wiki/2^n mod n">2^n mod n</a>
%F A296369 a(n) = A055685(n) - 1.
%t A296369 Select[Range[10^5], Divisible[2^(# + 1) + 1, #] &] (* _Robert Price_, Oct 11 2018 *)
%o A296369 (Python)
%o A296369 A296369_list = [n for n in range(1,10**6) if pow(2,n+1,n) == n-1] # _Chai Wah Wu_, Nov 04 2019
%Y A296369 Solutions to 2^m == k (mod m): A296370 (k=3/2), A187787 (k=1/2), this sequence (k=-1/2), A000079 (k=0), A006521 (k=-1), A015919 (k=2), A006517 (k=-2), A050259 (k=3), A015940 (k=-3), A015921 (k=4), A244673 (k=-4), A128121 (k=5), A245318 (k=-5), A128122 (k=6), A245728 (k=-6), A033981 (k=7), A240941 (k=-7), A015922 (k=8), A245319 (k=-8), A051447 (k=9), A240942 (k=-9), A128123 (k=10), A245594 (k=-10), A033982 (k=11), A128124 (k=12), A051446 (k=13), A128125 (k=14), A033983 (k=15), A015924 (k=16), A124974 (k=17), A128126 (k=18), A125000 (k=19), A015925 (k=2^5), A015926 (k=2^6), A015927 (k=2^7), A015929 (k=2^8), A015931 (k=2^9), A015932 (k=2^10), A015935 (k=2^11), A015937 (k=2^12)
%K A296369 nonn
%O A296369 1,2
%A A296369 _Max Alekseyev_, Dec 10 2017
%E A296369 Incorrect term 4285389 removed by _Chai Wah Wu_, Nov 04 2019