A128122 Numbers m such that 2^m == 6 (mod m).

1, 2, 10669, 6611474, 43070220513807782

Offset

1,2

Comments

No other terms below 10^17. - Max Alekseyev, Nov 18 2022

A large term: 862*(2^861-3)/281437921287063162726198552345362315020202285185118249390789 (203 digits). - Max Alekseyev, Sep 24 2016

Links

Table of n, a(n) for n=1..5.

Joe K. Crump, 2^n mod n

OEIS Wiki, 2^n mod n

Example

2 == 6 (mod 1), so 1 is a term;
4 == 6 (mod 2), so 2 is a term.

Mathematica

m = 6; Join[Select[Range[m], Divisible[2^# - m, #] &],
Select[Range[m + 1, 10^6], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 08 2018 *)

Crossrefs

Solutions to 2^m == k (mod m): A000079 (k=0),A187787 (k=1/2), A296369 (k=-1/2), A006521 (k=-1), A296370 (k=3/2), A015919 (k=2), A006517 (k=-2), A050259 (k=3), A015940 (k=-3), A015921 (k=4), A244673 (k=-4), A128121 (k=5), A245318 (k=-5), this sequence (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)

Cf. A015910, A036236.

Sequence in context: A294324 A349510 A134656 * A082178 A345396 A287650

Adjacent sequences: A128119 A128120 A128121 * A128123 A128124 A128125

Keyword

hard,more,nonn

Author

Alexander Adamchuk, Feb 15 2007

Extensions

1 and 2 added by N. J. A. Sloane, Apr 23 2007

a(5) from Max Alekseyev, Nov 18 2022

Status

approved