A069927 -id:A069927 - cp's OEIS frontend

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

Franz Vrabec, Jan 06 2013

nonn

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.

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

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

Cf. A055685, A069927, A112983.

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

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 *)

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

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

A115976 Numbers k that divide 2^(k-2) + 1.

Original entry on oeis.org

1, 3, 49737, 717027, 9723611, 21335267, 32390921, 38999627, 43091897, 86071337, 101848553, 102361457, 228911411, 302948067, 370219467, 393664027, 455781089, 483464027, 1040406177, 1272206987, 2371678553, 2571052241, 2648052857, 3054713937, 3597613307, 3782971499, 3917903851, 4005163577, 5419912241

Offset: 1

Max Alekseyev, Mar 15 2006

nonn

Some larger terms: 4465786944074559659, 1440261542571735083956640176981881665928575750093930787551969

Max Alekseyev, Table of n, a(n) for n = 1..708 (contains all terms below 10^15)

The odd elements of A244673.

Cf. A006521, A006517, A069927, A067945, A067946, A067947, A068382, A068383, A014945, A014946, A014949, A092028.

lst = {}; Do[ If[ PowerMod[2, 2n - 3, 2n - 1] == 2n - 2, AppendTo[lst, 2n - 1]], {n, 10^9}]; lst (* Robert G. Wilson v, Apr 04 2006 *)

More terms from Robert G. Wilson v, Apr 04 2006
Terms a(24) onward from Max Alekseyev, Feb 03 2015
b-file corrected and extended by Max Alekseyev, Oct 27 2018

A381010 Positive integers k such that 2^(k+2) - 1 is divisible by k.

Original entry on oeis.org

1, 7, 511, 713, 11023, 15553, 43873, 81079, 95263, 323593, 628153, 2275183, 6520633, 6955513, 7947583, 10817233, 12627943, 14223823, 15346303, 19852423, 27923663, 28529473, 29360527, 31019623, 39041863, 41007823, 79015273, 134217727, 143998193, 213444943, 227018383

Offset: 1

Oisín Flynn-Connolly, Apr 10 2025

nonn

7 is the only prime term.

Cf. A000225, A055685, A069927, A187787.

q:= k-> 0=(2&^(k+2)-1) mod k:
select(q, [$1..1000000])[];  # Alois P. Heinz, Apr 10 2025

isok(k) = Mod(2, k)^(k+2) == 1; \\ Michel Marcus, Apr 10 2025

def in_sequence(n):
    return pow(2, n + 2, n) == 1 % n

cp's OEIS Frontend

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

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A115976 Numbers k that divide 2^(k-2) + 1.

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Mathematica

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A381010 Positive integers k such that 2^(k+2) - 1 is divisible by k.

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Maple

PARI

Python