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A296716 Numbers congruent to {7, 11, 13, 29} mod 30.

%I A296716 #25 Sep 08 2022 08:46:20
%S A296716 7,11,13,29,37,41,43,59,67,71,73,89,97,101,103,119,127,131,133,149,
%T A296716 157,161,163,179,187,191,193,209,217,221,223,239,247,251,253,269,277,
%U A296716 281,283,299,307,311,313,329,337,341,343,359,367,371,373,389,397,401,403
%N A296716 Numbers congruent to {7, 11, 13, 29} mod 30.
%C A296716 For any m >= 0, if F(m) = 2^(2^m) + 1 has a factor of the form b = a(n)*2^k + 1 with k >= m + 2 and n >= 1, then the integer F(m)/b is congruent to 13 or 19 mod 30.
%H A296716 Colin Barker, <a href="/A296716/b296716.txt">Table of n, a(n) for n = 1..1000</a>
%H A296716 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A296716 a(n) = a(n-1) + a(n-4) - a(n-5), n >= 6.
%F A296716 a(n) = a(n-4) + 30.
%F A296716 G.f.: x*(7 + 4*x + 2*x^2 + 16*x^3 + x^4)/((1 + x)*(1 + x^2)*(1 - x)^2).
%F A296716 a(n) = (-15 + 5*(-1)^n + (3+9*i)*(-i)^n + (3-9*i)*i^n + 30*n) / 4 where i=sqrt(-1). - _Colin Barker_, Dec 19 2017
%F A296716 E.g.f.: (5*(e^(-x) + (6*x - 3)*e^x) + 6*cos(x) + 18*sin(x))/4. - _Iain Fox_, Dec 19 2017
%t A296716 LinearRecurrence[{1, 0, 0, 1, -1}, {7, 11, 13, 29, 37}, 60]
%o A296716 (Magma) [n: n in [0..403] | n mod 30 in {7, 11, 13, 29}];
%o A296716 (PARI) Vec(x*(7 + 4*x + 2*x^2 + 16*x^3 + x^4)/((1 + x)*(1 + x^2)*(1 - x)^2 + O(x^55)))
%Y A296716 Cf. A191062, A267985.
%K A296716 nonn,easy
%O A296716 1,1
%A A296716 _Arkadiusz Wesolowski_, Dec 19 2017