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

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

Chai Wah Wu, Table of n, a(n) for n = 1..1192

OEIS Wiki, 2^n mod n

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

Adjacent sequences: A296366 A296367 A296368 * A296370 A296371 A296372

Keyword

nonn

Author

Max Alekseyev, Dec 10 2017

Extensions

Incorrect term 4285389 removed by Chai Wah Wu, Nov 04 2019

Status

approved