A293862 Sequence of signed integers where each is chosen to be as small as possible (in absolute value) subject to the condition that no three terms a(j), a(j+k), a(j+2k) (for any j and k) form an arithmetic progression; in case of a tie, preference is given to the positive value.

0, 0, 1, 0, 0, 1, 1, -1, -1, 0, 0, -1, 0, 0, 1, 3, 3, -1, 3, 3, 1, 1, 2, 2, 1, -3, 2, 0, 0, -2, 0, 0, 1, -3, -3, -2, 0, 0, 4, 0, 0, 1, -2, -1, -1, -2, 5, -1, 3, -3, 2, 3, 3, 2, 5, 4, 4, 2, 4, 2, 3, -1, -1, 3, -8, -2, 5, 2, -2, -2, -8, -3, -2, -8, -6, -6, 2, 5

Offset: 1

Author

Rémy Sigrist, Oct 18 2017

Keywords

• sign

Comments

This sequence is a "signed" variant of A229037. Graphically, both sequences have similar ethereal features.

For any n > 0, |a(n)| <= floor( (n+1)/4 ).

Examples

			a(1) = 0 is suitable.
a(2) = 0 is suitable.
a(3) cannot equal 0 as 2*a(3-1) - a(3-2) = 0.
a(3) = 1 is suitable.
a(4) cannot equal 2 as 2*a(4-1) - a(4-2) = 2.
a(4) = 0 is suitable.
a(5) cannot equal -1 as 2*a(5-1) - a(5-2) = -1.
a(5) cannot equal 2 as 2*a(5-2) - a(5-4) = 2.
a(5) = 0 is suitable.
a(6) cannot equal 0 as 2*a(6-1) - a(6-2) = 0.
a(6) = 1 is suitable.
a(7) cannot equal 2 as 2*a(7-1) - a(7-2) = 2.
a(7) cannot equal -1 as 2*a(7-2) - a(7-4) = -1.
a(7) cannot equal 0 as 2*a(7-3) - a(7-6) = 0.
a(7) = 1 is suitable.
a(8) cannot equal 1 as 2*a(8-1) - a(8-2) = 1.
a(8) cannot equal 2 as 2*a(8-2) - a(8-4) = 2.
a(8) cannot equal 0 as 2*a(8-3) - a(8-6) = 0.
a(8) = -1 is suitable.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..100000
• Rémy Sigrist, Scatterplot of the first 1000000 terms
• Rémy Sigrist, C++ program for A293862