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Numbers k that divide 2^(k-1) - 2.
3

%I #43 Nov 10 2023 09:23:52

%S 1,2,6,10,14,22,26,30,34,38,46,58,62,74,82,86,94,106,118,122,134,142,

%T 146,158,166,170,178,182,194,202,206,214,218,226,254,262,274,278,298,

%U 302,314,326,334,346,358,362,382,386,394,398,422,446,454,458,466,478,482,502,514,526,538,542,554,562,566,586,614,622,626

%N Numbers k that divide 2^(k-1) - 2.

%H Amiram Eldar, <a href="/A192109/b192109.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Reinhard Zumkeller)

%t Join[{1,2},Select[Range[700],PowerMod[2,#-1,#]==2&]] (* _Harvey P. Dale_, May 15 2015 *)

%o (Haskell)

%o import Data.List (elemIndices)

%o a192109 n = a192109_list !! (n-1)

%o a192109_list = map (+ 1) $ elemIndices 0 $ zipWith mod a000918_list [1..]

%o -- _Reinhard Zumkeller_, Apr 23 2013

%o (PARI) is(n)=Mod(2,n)^(n-1)==2 \\ _Charles R Greathouse IV_, Nov 04 2016

%Y Contains A216090 as subsequence.

%Y Subsequence of A015921, consisting of the terms that are not multiples of 4.

%Y The odd terms form A173572.

%Y Cf. A014741, A000918.

%K nonn

%O 1,2

%A _Max Alekseyev_, Apr 22 2013