A081502 - OEIS

%I #28 Dec 05 2019 04:42:00

%S 0,1,2,3,4,5,6,7,8,9,3,4,5,6,7,8,9,10,11,12,6,7,8,9,10,11,12,13,14,15,

%T 9,10,11,12,13,14,15,16,17,18,12,13,14,15,16,17,18,19,20,21,15,16,17,

%U 18,19,20,21,22,23,24,18,19,20,21,22,23,24,25,26,27,21,22,23,24,25,26,27,28,29

%N Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 3x+y.

%C Eswaran observes that n is divisible by 7 iff repeated application of a ends at the number 7.

%C a(n) is divisible by 7 iff n is divisible by 7: e.g., a(7) = a(14) = a(21) = 7, a(28) = a(35) = a(42) = 14 etc. - _Zak Seidov_, Mar 19 2014

%D R. Eswaran, Test of divisibility of the number 7, Abstracts Amer. Math. Soc., 23 (No. 2, 2002), #974-00-5, p. 275.

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,1,-1).

%F G.f.: -x*(6*x^9-x^8-x^7-x^6-x^5-x^4-x^3-x^2-x-1) / (x^11-x^10-x+1). - _Colin Barker_, Mar 19 2014

%F a(n) = n-7*floor(n/10). - _Wesley Ivan Hurt_, May 12 2016

%p A081502 := proc(n)

%p     local x,y ;

%p     y := modp(n,10) ;

%p     x := iquo(n,10) ;

%p     3*x+y ;

%p end proc:

%p seq(A081502(n),n=0..120) ; # _R. J. Mathar_, Oct 03 2014

%t Table[n - 7 * Floor[n / 10], {n, 0, 100}] (* _Joshua Oliver_, Dec 04 2019 *)

%o (PARI) a(n) = 3*(n\10) + (n % 10); \\ _Michel Marcus_, Mar 19 2014

%o (PARI) a(n) = [3,1]*divrem(n,10); \\ _Kevin Ryde_, Dec 04 2019

%Y Different from A028898 for n>=100 (e.g. a(111) = 34, A029989(111) = 13).

%Y Cf. A081503, A081594, A081595, A081596, A081597, A081598, A081599, A081600.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Apr 22 2003