A155751 A variation on 10^n mod 17.

1, -7, -2, -3, 4, 6, -8, 5, -1, 7, 2, 3, -4, -6, 8, -5, 1, -7, -2, -3, 4, 6, -8, 5, -1, 7, 2, 3, -4, -6, 8, -5, 1, -7, -2, -3, 4, 6, -8, 5, -1, 7, 2, 3, -4, -6, 8, -5, 1, -7, -2, -3, 4, 6, -8, 5, -1, 7, 2, 3, -4, -6, 8, -5, 1, -7, -2, -3, 4, 6, -8, 5, -1, 7, 2, 3, -4, -6, 8, -5

Offset: 0

Author

Ferruccio Guidi (fguidi(AT)cs.unibo.it), Jan 26 2009, Feb 08 2009

Keywords

• easy
• sign

Comments

This is 10^n mod 17, using values -8,-7,...,7,8 (instead of 0..16). - Don Reble, Sep 02 2017.

This sequence can be employed in a test for divisibility by 17 and works like A033940 works for 7.

The use of negative coefficients ensures the termination of the test because the modulus of the intermediate sum at each step of the test decreases strictly.

The test is successful if the final sum is 0.

The negative coefficients have the form (10^n mod 17) - 17 when 10^n mod 17 > 8.

Example: 9996 is divisible by 17 since |6*1 + 9*(-7) + 9*(-2) + 9*(-3)| = 102 and 2*1 + 0*(-7) + 1*(-2) = 0.

Crossrefs

Cf. A033940, A119910, A117378.

Formula

a(n)= -a(n-8). G.f.:(1-7x-2x^2-3x^3+4x^4+6x^5-8x^6+5x^7)/(1+x^8). [From R. J. Mathar, Feb 13 2009]