A267984 - OEIS

%I #18 Sep 10 2022 07:36:06

%S 17,23,47,53,77,83,107,113,137,143,167,173,197,203,227,233,257,263,

%T 287,293,317,323,347,353,377,383,407,413,437,443,467,473,497,503,527,

%U 533,557,563,587,593,617,623,647,653,677,683,707,713,737,743,767,773

%N Numbers congruent to {17, 23} mod 30.

%C Union of A128468 and A128473.

%C 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 Colin Barker, <a href="/A267984/b267984.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F a(n) = a(n-1) + a(n-2) - a(n-3), n >= 4.

%F G.f.: x*(17 + 6*x + 7*x^2)/((1 + x)*(1 - x)^2).

%F a(n) = a(n-2) + 30.

%F a(n) = 10*(3*n - 2) - a(n-1).

%F From _Colin Barker_, Jan 24 2016: (Start)

%F a(n) = (30*n - 9*(-1)^n - 5)/2 for n>0.

%F a(n) = 15*n - 7 for n>0 and even.

%F a(n) = 15*n + 2 for n odd.

%F (End)

%F E.g.f.: 7 + ((30*x - 5)*exp(x) - 9*exp(-x))/2. - _David Lovler_, Sep 10 2022

%t LinearRecurrence[{1, 1, -1}, {17, 23, 47}, 52]

%o (Magma) [n: n in [0..773] | n mod 30 in {17, 23}];

%o (PARI) Vec(x*(17 + 6*x + 7*x^2)/((1 + x)*(1 - x)^2) + O(x^53))

%Y Cf. A128468, A128473, A267985.

%K nonn,easy

%O 1,1

%A _Arkadiusz Wesolowski_, Jan 23 2016