OFFSET
0,2
COMMENTS
Delete the last digit from n and subtract twice this digit from the shortened number. - N. J. A. Sloane, May 25 2019
(n==0 modulo 7) iff (a(n)==0 modulo 7); applied recursively, this property provides a useful test for divisibility by 7.
REFERENCES
Erdős, Paul, and János Surányi. Topics in the Theory of Numbers. New York: Springer, 2003. Problem 6, page 3.
Karl Menninger, Rechenkniffe, Vandenhoeck & Ruprecht in Goettingen (1961), 79A.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Divisibility Tests.
Wikipedia, Divisibility rule
FORMULA
From R. J. Mathar, Nov 23 2010: (Start)
a(n) = a(n-1) + a(n-10) - a(n-11).
G.f.: x*(-2 -2*x -2*x^2 -2*x^3 -2*x^4 -2*x^5 -2*x^6 -2*x^7 -2*x^8 +19*x^9)/((1+x)*(x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1)*(x-1)^2). (End)
EXAMPLE
695591 is not a multiple of 7, as 695591 -> 69559-2*1=69557 -> 6955-2*7=6941 -> 694-2*1=692 -> 69-2*2=65=7*9+2, therefore the answer is NO.
Is 3206 divisible by 7? 3206 -> 320-2*6=308 -> 30-2*8=14=7*2, therefore the answer is YES, indeed 3206=2*7*229.
MATHEMATICA
Table[Floor[n/10] - 2*Mod[n, 10], {n, 0, 100}] (* G. C. Greubel, Apr 07 2016 *)
PROG
(Haskell)
a076309 n = n' - 2 * m where (n', m) = divMod n 10
-- Reinhard Zumkeller, Jun 01 2013
(PARI) a(n) = n\10 - 2*(n % 10); \\ Michel Marcus, Apr 07 2016
CROSSREFS
KEYWORD
sign
AUTHOR
Reinhard Zumkeller, Oct 06 2002
STATUS
approved