login
This site is supported by donations to The OEIS Foundation.

 

Logo

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.

License Agreements, Terms of Use, Privacy Policy. .

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