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%I #28 Dec 14 2019 16:38:12
%S 1,19,37,73,91,109,127,163,181,199,217,253,271,289,307,343,361,379,
%T 397,433,451,469,487,523,541,559,577,613,631,649,667,703,721,739,757,
%U 793,811,829,847,883,901,919,937,973,991,1009,1027,1063,1081,1099
%N Numbers not divisible by 2, 3 or 5 (A007775) with digital root 1.
%C Numbers == {1, 19, 37, 73} mod 90 with additive sum sequence 1{+18+18+36+18} {repeat ...}. Includes all prime numbers > 7 with digital root 1.
%H Colin Barker, <a href="/A301617/b301617.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 n == {1, 19, 37, 73} mod 90.
%F a(n + 1) = a(n) + 18 * A177704(n + 1). - _David A. Corneth_, Mar 24 2018
%F From _Colin Barker_, Mar 24 2018: (Start)
%F G.f.: x*(1 + 18*x + 18*x^2 + 36*x^3 + 17*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 1+18=19; 19+18=37; 37+36=73; 73+18=91; 91+18=109.
%p seq(seq(i+90*j,i=[1,19,37,73]),j=0..30); # _Robert Israel_, Mar 25 2018
%t LinearRecurrence[{1,0,0,1,-1},{1,19,37,73,91},50] (* _Harvey P. Dale_, Dec 14 2019 *)
%o (PARI) a(n) = 1 + 18 * (n - 1 + n\4) \\ _David A. Corneth_, Mar 24 2018
%o (PARI) Vec(x*(1 + 18*x + 18*x^2 + 36*x^3 + 17*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ _Colin Barker_, Mar 24 2018
%Y Cf. A177704, A045572.
%Y Intersection of A007775 and A017173.
%K nonn,base,easy
%O 1,2
%A _Gary Croft_, Mar 24 2018
%E The missing term 1081 added to the sequence by _Colin Barker_, Mar 24 2018
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