A082802 - OEIS

%I #14 Mar 23 2017 06:20:38

%S 14,21,35,42,56,63,7,84,91,105,112,126,133,14,154,161,175,182,196,203,

%T 21,224,231,245,252,266,273,28,294,301,315,322,336,343,35,364,371,385,

%U 392,406,413,42,434,441,455,462,476,483,49,504,511,525,532,546,553,56

%N Smallest multiple of 7 beginning with n.

%H Vincenzo Librandi, <a href="/A082802/b082802.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,2,0,0,0,0,0,0,-1).

%F From _Colin Barker_, Mar 23 2017: (Start)

%F G.f.: 7*x*(2 + 3*x + 5*x^2 + 6*x^3 + 8*x^4 + 9*x^5 + x^6 + 8*x^7 + 7*x^8 + 5*x^9 + 4*x^10 + 2*x^11 + x^12) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)^2).

%F a(n) = 2*a(n-7) - a(n-14) for n>14.

%F (End)

%t Table[If[Mod[n, 7]==0, n, If[Mod[10 n, 7]==0, 10 n, 10 n + 7 - Mod[10 n, 7]]], {n, 56}] (* _Ray Chandler_, Feb 09 2014 *)

%o (PARI) Vec(7*x*(2 + 3*x + 5*x^2 + 6*x^3 + 8*x^4 + 9*x^5 + x^6 + 8*x^7 + 7*x^8 + 5*x^9 + 4*x^10 + 2*x^11 + x^12) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)^2) + O(x^60)) \\ _Colin Barker_, Mar 23 2017

%Y Cf. A082799, A082800, A082801, A082803, A082804.

%K nonn,base,easy

%O 1,1

%A _Amarnath Murthy_, Apr 20 2003

%E Corrected a(3)=35 and extended by _Ray Chandler_, Feb 09 2014

%E Typo in Mathematica program fixed by _Vincenzo Librandi_, Feb 10 2014