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A136805
Squares mod 65537.
5
0, 1, 2, 4, 8, 9, 13, 15, 16, 17, 18, 19, 21, 25, 26, 30, 32, 33, 34, 35, 36, 37, 38, 42, 49, 50, 52, 53, 55, 60, 64, 66, 68, 69, 70, 71, 72, 74, 76, 77, 79, 81, 84, 87, 93, 97, 98, 100, 103, 104, 106, 107, 109, 110, 115, 117, 120, 121, 123, 128, 129, 132, 135
OFFSET
1,3
COMMENTS
Because 65537 is a Fermat prime, the complement of this set, A136806, is the set of primitive roots (mod 65537).
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 1..32769 (full sequence)
FORMULA
a(n) + a(32771 - n) = 65537 for n > 1.
MAPLE
A136805:={}: for n from 0 to 65536 do A136805 := A136805 union {n^2 mod 65537}: od: l:=sort(convert(A136805, list)): l[1..63]; # Nathaniel Johnston, Jun 23 2011
MATHEMATICA
p = 65537; Select[Range[0, p - 1], JacobiSymbol[#, p] == 1 &]
PROG
(Sage) [quadratic_residues(65537)] # Zerinvary Lajos, May 24 2009
(PARI) A136805=Set([k^2 | k <- [0..2^16]]%65537); \\ M. F. Hasler, Nov 15 2017
(Scala) ((1: BigInt) to (65537: BigInt)).map(n => (n * n) % 65537).toSet.toSeq.sorted // Alonso del Arte, Dec 17 2019
CROSSREFS
Cf. A136806 (nonsquares mod 65537); A136803 and A136804 ((non)squares mod 257).
Cf. A010379.
Sequence in context: A033858 A010379 A010395 * A372894 A035258 A115813
KEYWORD
fini,full,easy,nonn
AUTHOR
T. D. Noe, Jan 22 2008
STATUS
approved