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A296369
Numbers m such that 2^m == -1/2 (mod m).
11
1, 5, 65, 377, 1189, 1469, 25805, 58589, 134945, 137345, 170585, 272609, 285389, 420209, 538733, 592409, 618449, 680705, 778805, 1163065, 1520441, 1700945, 2099201, 2831009, 4020029, 4174169, 4516109, 5059889, 5215769
OFFSET
1,2
COMMENTS
Equivalently, 2^(m+1) == -1 (mod m), or m divides 2^(m+1) + 1.
The sequence is infinite, see A055685.
LINKS
FORMULA
a(n) = A055685(n) - 1.
MATHEMATICA
Select[Range[10^5], Divisible[2^(# + 1) + 1, #] &] (* Robert Price, Oct 11 2018 *)
PROG
(Python)
A296369_list = [n for n in range(1, 10**6) if pow(2, n+1, n) == n-1] # Chai Wah Wu, Nov 04 2019
CROSSREFS
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)
Sequence in context: A093195 A292228 A195579 * A061184 A118004 A281232
KEYWORD
nonn
AUTHOR
Max Alekseyev, Dec 10 2017
EXTENSIONS
Incorrect term 4285389 removed by Chai Wah Wu, Nov 04 2019
STATUS
approved