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A047299 Numbers that are congruent to {0, 1, 3, 4, 6} mod 7. 4

%I

%S 0,1,3,4,6,7,8,10,11,13,14,15,17,18,20,21,22,24,25,27,28,29,31,32,34,

%T 35,36,38,39,41,42,43,45,46,48,49,50,52,53,55,56,57,59,60,62,63,64,66,

%U 67,69,70,71,73,74,76,77,78

%N Numbers that are congruent to {0, 1, 3, 4, 6} mod 7.

%C Nonnegative m such that floor(k*m^2/7) = k*floor(m^2/7), where k = 2 or 3. [_Bruno Berselli_, Dec 03 2015]

%C For k > 1 (A007530(k+1) - A007530(k))/30 is a term in this sequence. - _Hugo Pfoertner_, May 29 2020

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).

%F G.f.: x^2*(1+2*x+x^2+2*x^3+x^4) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - _R. J. Mathar_, Oct 25 2011

%F a(n) = floor((7n-5)/5). - _Lorenz H. Menke, Jr._, Jun 19 2013

%t a[n_]:=Floor[(7n-5)/5]; Table[a[i],{i,1,30}]; (* _Lorenz H. Menke, Jr._, Jun 19 2013 *)

%o (PARI) a(n)=(7*n-5)\5 \\ _Charles R Greathouse IV_, Jun 19 2013

%o (MAGMA) [Floor((7*n-5)/5): n in [1..100]]; // _Zaki Khandaker_, Jun 21 2015

%Y Cf. A007530 (prime quadruples).

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_

%E Formula and programs adapted to offset 1 by _Michel Marcus_, May 30 2020

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Last modified April 13 03:43 EDT 2021. Contains 342934 sequences. (Running on oeis4.)