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A015919
Positive integers k such that 2^k == 2 (mod k).
32
1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 341, 347, 349, 353, 359, 367
OFFSET
1,2
COMMENTS
Includes 341 which is first pseudoprime to base 2 and distinguishes sequence from A008578.
First composite even term is a(14868) = 161038 = A006935(2). - Max Alekseyev, Feb 11 2015
If k is a term, then so is 2^k - 1. - Max Alekseyev, Sep 22 2016
Terms of the form 2^k - 2 correspond to k in A296104. - Max Alekseyev, Dec 04 2017
If 2^k - 1 is a term, then so is k. - Thomas Ordowski, Apr 27 2018
LINKS
FORMULA
Equals {1} U A000040 U A001567 U A006935 = A001567 U A006935 U A008578. - Ray Chandler, Dec 07 2003; corrected by Max Alekseyev, Feb 11 2015
MATHEMATICA
Prepend[ Select[ Range@370, PowerMod[2, #, #] == 2 &], {1, 2}] // Flatten (* Robert G. Wilson v, May 16 2018 *)
PROG
(PARI) is(n)=Mod(2, n)^n==2 \\ Charles R Greathouse IV, Mar 11 2014
(Python)
def ok(n): return pow(2, n, n) == 2%n
print([k for k in range(1, 400) if ok(k)]) # Michael S. Branicky, Jun 03 2022
CROSSREFS
Contains A002997 as a subsequence.
The odd terms form A176997.
Sequence in context: A216886 A273960 A100726 * A352190 A324050 A064555
KEYWORD
nonn
STATUS
approved