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%I #19 Sep 21 2019 14:37:00
%S 7,43,61,79,97,133,151,169,187,223,241,259,277,313,331,349,367,403,
%T 421,439,457,493,511,529,547,583,601,619,637,673,691,709,727,763,781,
%U 799,817,853,871,889,907,943,961,979,997,1033,1051,1069,1087,1123
%N Numbers not divisible by 2, 3 or 5 (A007775) with digital root 7.
%C Numbers == {7, 43, 61, 79} mod 90 with additive sum sequence 7{+36+18+18+18} {repeat ...}. Includes all prime numbers > 5 with digital root 7.
%H Colin Barker, <a href="/A301628/b301628.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F Numbers == {7, 43, 61, 79} mod 90.
%F From _Colin Barker_, Sep 21 2019: (Start)
%F G.f.: x*(7 + 36*x + 18*x^2 + 18*x^3 + 11*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)).
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F (End)
%e 7+36=43; 43+18=61; 61+18=79; 79+18=97; 97+36=133.
%o (GAP) Filtered(Filtered([1..1200],n->n mod 2 <> 0 and n mod 3 <> 0 and n mod 5 <> 0),i->i-9*Int((i-1)/9)=7); # _Muniru A Asiru_, Apr 22 2018
%o (PARI) Vec(x*(7 + 36*x + 18*x^2 + 18*x^3 + 11*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^40)) \\ _Colin Barker_, Sep 21 2019
%Y Intersection of A007775 and A017245.
%K nonn,base,easy
%O 1,1
%A _Gary Croft_, Mar 24 2018
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