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A176033
Numbers n such that 2^(2n-1) == 2 (mod 2n) and such that 2^(n-1) != 1 (mod n).
4
15, 85, 91, 435, 451, 703, 1247, 1271, 1581, 1695, 1891, 2071, 3133, 3367, 3683, 4795, 4859, 5551, 6643, 8695, 9061, 9131, 9211, 9605, 9919, 12403, 13019, 14351, 14701, 15051, 15211, 16021, 16471, 19669, 20191, 20485, 24727, 25351, 26335, 26599, 27511, 28645
OFFSET
1,1
COMMENTS
The associated value k = (2^(n-1) mod n) satisfy 1 < gcd(k-1, n) < n.
The selection criterion 2^(2n-1) == 2 (mod 2n) admits 3, 5, 7, 11, 13, 15, 17, etc.
Expect that the sequences will be infinite only if the criterion has the form 2^(2n-1) == 2^k (mod 2n) where k - an integer (1, 2, ...), otherwise the sequence will be limited. For example, for criterion 2^(2n-1) == 14 (mod 2n), the sequence begins 9, 27, 7281, 19143.
LINKS
MAPLE
select(n -> 2 &^ (2*n-1) - 2 mod (2*n) = 0 and 2 &^ (n-1) -1 mod n <> 0, [seq(n, n=3..10^5, 2)]); # Robert Israel, Nov 06 2017
PROG
(PARI) alist(m) = {for (n=1, m, v = 2^(2*n-1); if ((v % (2*n) == 2), k = 2^(n-1) % n; if (k > 1, print1(n, ", "); ); ); ); } \\ Michel Marcus, Jan 24 2013
CROSSREFS
Set difference of A020136 and A001567. - Max Alekseyev, Nov 06 2017
Sequence in context: A281189 A206383 A020136 * A067401 A206169 A160599
KEYWORD
nonn
AUTHOR
Alzhekeyev Ascar M, Dec 06 2010
EXTENSIONS
More terms from Michel Marcus, Jan 24 2013
STATUS
approved