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A267985 Numbers congruent to {7, 13} mod 30.

%I A267985 #26 Sep 10 2022 07:36:00
%S A267985 7,13,37,43,67,73,97,103,127,133,157,163,187,193,217,223,247,253,277,
%T A267985 283,307,313,337,343,367,373,397,403,427,433,457,463,487,493,517,523,
%U A267985 547,553,577,583,607,613,637,643,667,673,697,703,727,733,757,763
%N A267985 Numbers congruent to {7, 13} mod 30.
%C A267985 Union of A128471 and A082369.
%C A267985 For all k >= 1 the numbers 2^k - a(n) and a(n)*2^k - 1 do not form a pair of primes, where n is any positive integer.
%H A267985 Colin Barker, <a href="/A267985/b267985.txt">Table of n, a(n) for n = 1..1000</a>
%H A267985 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A267985 a(n) = a(n-1) + a(n-2) - a(n-3), n >= 4.
%F A267985 G.f.: x*(7 + 6*x + 17*x^2)/((1 + x)*(1 - x)^2).
%F A267985 a(n) = a(n-2) + 30.
%F A267985 a(n) = 10*(3*n - 4) - a(n-1).
%F A267985 From _Colin Barker_, Jan 24 2016: (Start)
%F A267985 a(n) = (30*n-9*(-1)^n-25)/2 for n>0.
%F A267985 a(n) = 15*n-17 for n>0 and even.
%F A267985 a(n) = 15*n-8 for n odd.
%F A267985 (End)
%F A267985 E.g.f.: 17 + ((30*x - 25)*exp(x) - 9*exp(-x))/2. - _David Lovler_, Sep 10 2022
%t A267985 LinearRecurrence[{1, 1, -1}, {7, 13, 37}, 52]
%o A267985 (Magma) [n: n in [0..763] | n mod 30 in {7, 13}];
%o A267985 (PARI) Vec(x*(7 + 6*x + 17*x^2)/((1 + x)*(1 - x)^2) + O(x^53))
%Y A267985 Cf. A082369, A128471, A267984.
%K A267985 nonn,easy
%O A267985 1,1
%A A267985 _Arkadiusz Wesolowski_, Jan 23 2016
%E A267985 Comment corrected by _Philippe Deléham_, Nov 28 2016