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

0,2

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.

Links

Table of n, a(n) for n=0..79.

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]

Crossrefs

Cf. A033940, A119910, A117378.

Sequence in context: A222224 A163333 A116369 * A092234 A160101 A210975

Adjacent sequences: A155748 A155749 A155750 * A155752 A155753 A155754

Keyword

easy,sign

Author

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

Status

approved