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A267984 Numbers congruent to {17, 23} mod 30.

%I A267984 #18 Sep 10 2022 07:36:06
%S A267984 17,23,47,53,77,83,107,113,137,143,167,173,197,203,227,233,257,263,
%T A267984 287,293,317,323,347,353,377,383,407,413,437,443,467,473,497,503,527,
%U A267984 533,557,563,587,593,617,623,647,653,677,683,707,713,737,743,767,773
%N A267984 Numbers congruent to {17, 23} mod 30.
%C A267984 Union of A128468 and A128473.
%C A267984 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 A267984 Colin Barker, <a href="/A267984/b267984.txt">Table of n, a(n) for n = 1..1000</a>
%H A267984 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A267984 a(n) = a(n-1) + a(n-2) - a(n-3), n >= 4.
%F A267984 G.f.: x*(17 + 6*x + 7*x^2)/((1 + x)*(1 - x)^2).
%F A267984 a(n) = a(n-2) + 30.
%F A267984 a(n) = 10*(3*n - 2) - a(n-1).
%F A267984 From _Colin Barker_, Jan 24 2016: (Start)
%F A267984 a(n) = (30*n - 9*(-1)^n - 5)/2 for n>0.
%F A267984 a(n) = 15*n - 7 for n>0 and even.
%F A267984 a(n) = 15*n + 2 for n odd.
%F A267984 (End)
%F A267984 E.g.f.: 7 + ((30*x - 5)*exp(x) - 9*exp(-x))/2. - _David Lovler_, Sep 10 2022
%t A267984 LinearRecurrence[{1, 1, -1}, {17, 23, 47}, 52]
%o A267984 (Magma) [n: n in [0..773] | n mod 30 in {17, 23}];
%o A267984 (PARI) Vec(x*(17 + 6*x + 7*x^2)/((1 + x)*(1 - x)^2) + O(x^53))
%Y A267984 Cf. A128468, A128473, A267985.
%K A267984 nonn,easy
%O A267984 1,1
%A A267984 _Arkadiusz Wesolowski_, Jan 23 2016