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A280109 a(n) is the decimal value corresponding to the binary representation of the distribution of quadratic residues (value=1) and non-quadratic residues (value=0) mod n, where numbers are ordered left to right from 0 to n-1.

%I A280109 #35 Jun 08 2024 15:44:45
%S A280109 1,3,6,12,25,54,116,200,402,825,1762,3204,6925,14964,25904,51264,
%T A280109 119179,206226,424582,836616,1648692,3610338,8218192,13125760,
%U A280109 26518825,56736525,105587858,210503748,434671993,848848176,1995529252,3359686720,7257392290,15621149067
%N A280109 a(n) is the decimal value corresponding to the binary representation of the distribution of quadratic residues (value=1) and non-quadratic residues (value=0) mod n, where numbers are ordered left to right from 0 to n-1.
%C A280109 Sort mod n numbers {0,1,...,n-1} in ascending order. For each modular number i, write 1 if i is a quadratic residue mod n (i.e., it has a square root), else write 0. The corresponding n-bit number is a(n).
%H A280109 Adnan Baysal, <a href="/A280109/b280109.txt">Table of n, a(n) for n = 1..1000</a>
%e A280109 For n = 10, quadratic residues are 0, 1, 4, 5, 6, 9 so a(10) is 1100111001 in binary which is 825.
%t A280109 f[n_] := Total[ 2^(n -1 -Union[ Mod[ Range[0, n - 1]^2, n]] )]; Array[f, 34] (* _Robert G. Wilson v_, Dec 28 2016 *)
%o A280109 (Python)
%o A280109 def qr_distribution(N):
%o A280109     QR = []
%o A280109     QN = []
%o A280109     for i in range(N):
%o A280109         t = (i*i)%N
%o A280109         if t not in QR: QR.append(t)
%o A280109     for i in range(N):
%o A280109         if i not in QR: QN.append(i)
%o A280109     out = 0
%o A280109     for i in range(0,N):
%o A280109         out *= 2
%o A280109         if i in QR: out += 1
%o A280109     return out
%Y A280109 Cf. A055094, A080117, A080146, A096008.
%K A280109 nonn,base
%O A280109 1,2
%A A280109 _Adnan Baysal_, Dec 26 2016