This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A179417 #13 May 18 2024 14:52:11 %S A179417 1,5,24,104,279,2001,4131,17453,88826,362532,1655660,6120642,25376649, %T A179417 128526482,301370205,1756488602,8046359747,30854867177,73845140753, %U A179417 488906501177,2106640948770,6573967883049,29711211505300 %N A179417 a(n) is the binary number (shown here in decimal) constructed from quadratic residues of 65537 in range [(n^2)+1,(n+1)^2] in such a way that quadratic residues are mapped to 1-bits, and non-quadratic residues (as well as the multiples of 65537) to 0-bits, with the lower end of range mapped to less significant, and the higher end of range to more significant bits. %C A179417 The binary width of terms are 1, 3, 5, 7, 9, ... i.e., the successive odd numbers, as their partial sums give the squares, 1, 4, 9, 16, ... at which points there certainly is always a quadratic residue, which thus gives the most significant bit for each number. %H A179417 Antti Karttunen, <a href="/A179417/b179417.txt">Table of n, a(n) for n = 0..256</a> %H A179417 Antti Karttunen, <a href="/A179417/a179417_256.png">Terms a(0)-a(255) drawn as a bit triangle, 1 pixel per bit.</a> %H A179417 Antti Karttunen, <a href="/A179417/a179417_256_p2.png">Terms a(0)-a(255) drawn as a bit triangle, 2x2 pixels per bit.</a> %H A179417 Antti Karttunen, <a href="/A179417/a179417_256_p3.png">Terms a(0)-a(255) drawn as a bit triangle, 3x3 pixels per bit.</a> %e A179417 In the range [(2^2)+1, (2+1)^2] (i.e., [5,9]) we have A165471(5)=A165471(6)=A165471(7)=-1 and A165471(8)=A165471(9)=+1, i.e., there are quadratic non-residues at points 5, 6 and 7, and quadratic residues at 8 and 9, so we construct a binary number 11000, which is 24 in decimal, thus a(2)=24. %o A179417 (MIT/GNU Scheme) %o A179417 (define (A179417 n) (let ((ul (A005408 n))) (let loop ((i (A000290 n)) (j 0) (s 0)) (cond ((= j ul) s) ((= 0 (1+halved (A165471 (1+ i)))) (loop (1+ i) (1+ j) s)) (else (loop (1+ i) (1+ j) (+ s (expt 2 j)))))))) %o A179417 (define (1+halved n) (floor->exact (/ (1+ n) 2))) %Y A179417 Cf. A179418. %Y A179417 Compare to similar bit triangle illustrations given in A080070, A122229, A122232, A122235, A122239, A122242, A122245. %K A179417 nonn,base %O A179417 0,2 %A A179417 _Antti Karttunen_, Jul 27 2010