A187787 Numbers k such that 2^(k+1) == 1 (mod k).

1, 3, 15, 35, 119, 255, 455, 1295, 2555, 2703, 3815, 3855, 4355, 5543, 6479, 8007, 9215, 10439, 10619, 11951, 16211, 22895, 23435, 26319, 26795, 27839, 28679, 35207, 43055, 44099, 47519, 47879, 49679, 51119, 57239, 61919, 62567, 63167, 63935, 65535, 74447, 79055

Offset

1,2

Comments

Prime factorizations of the first ten terms: 3, 3*5, 5*7, 7*17, 3*5*17, 5*7*13, 5*7*37, 5*7*73, 3*17*53, 5*7*109.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

3 is in the sequence because 2^(3+1) mod 3 = 16 mod 3 = 1.

Maple

for n from 1 to 100000 do if 2&^(n+1) mod n = 1 then print(n) fi od;

Mathematica

m = 1; Join[Select[Range[1, m], Divisible[2^(# + 1), #] &],
Select[Range[m + 1, 10^5], PowerMod[2, # + 1, #] == m &]] (* Robert Price, Oct 11 2018 *)
Join[{1}, Select[Range[80000], PowerMod[2, #+1, #]==1&]] (* Harvey P. Dale, Aug 19 2019 *)

Prog

(PARI) for (n=1, 10^7, if (Mod(2, n)^(n+1)==1, print1(n, ", "))); /* Joerg Arndt, Jan 06 2013 */

Crossrefs

Cf. A055685, A069927, A112983.

Sequence in context: A015809 A293995 A015715 * A290717 A019009 A290716

Adjacent sequences: A187784 A187785 A187786 * A187788 A187789 A187790

Keyword

nonn

Author

Franz Vrabec, Jan 06 2013

Extensions

Term a(1)=1 prepended by Max Alekseyev, Nov 29 2014

Status

approved