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

Author

Franz Vrabec, Jan 06 2013

Keywords

• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A055685, A069927, A112983.

Programs

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 *)

PARI

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

Extensions

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