This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A076309 a(n) = floor(n/10) - 2*(n mod 10). 8
 0, -2, -4, -6, -8, -10, -12, -14, -16, -18, 1, -1, -3, -5, -7, -9, -11, -13, -15, -17, 2, 0, -2, -4, -6, -8, -10, -12, -14, -16, 3, 1, -1, -3, -5, -7, -9, -11, -13, -15, 4, 2, 0, -2, -4, -6, -8, -10, -12, -14, 5, 3, 1, -1, -3, -5, -7, -9, -11, -13, 6, 4, 2, 0, -2, -4, -6, -8, -10 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A008589, A076310, A076311, A076312. Sequence in context: A088116 A100817 A074157 * A088133 A115299 A076312 Adjacent sequences:  A076306 A076307 A076308 * A076310 A076311 A076312 KEYWORD sign AUTHOR Reinhard Zumkeller, Oct 06 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)