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.

1, 5, 24, 104, 279, 2001, 4131, 17453, 88826, 362532, 1655660, 6120642, 25376649, 128526482, 301370205, 1756488602, 8046359747, 30854867177, 73845140753, 488906501177, 2106640948770, 6573967883049, 29711211505300

Offset: 0

Author

Antti Karttunen, Jul 27 2010

Keywords

• nonn
• base

Comments

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.

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..256
• Antti Karttunen, Terms a(0)-a(255) drawn as a bit triangle, 1 pixel per bit.
• Antti Karttunen, Terms a(0)-a(255) drawn as a bit triangle, 2x2 pixels per bit.
• Antti Karttunen, Terms a(0)-a(255) drawn as a bit triangle, 3x3 pixels per bit.

Crossrefs

Cf. A179418.

Compare to similar bit triangle illustrations given in A080070, A122229, A122232, A122235, A122239, A122242, A122245.