%I #37 Sep 08 2022 08:46:10

%S 23,71,167,359,743,1511,3047,6119,12263,24551,49127,98279,196583,

%T 393191,786407,1572839,3145703,6291431,12582887,25165799,50331623,

%U 100663271,201326567,402653159,805306343,1610612711,3221225447,6442450919,12884901863,25769803751

%N a(1) = 23, a(2) = 71, a(n) = 3*a(n-1) - 2*a(n-2) for n>2.

%C The first 6 terms are prime, so are the 9th, 10th, 13th, 14th, 15th, 18th, 20th, and 26th.

%C Any term of the form a(7+n*10) appears to be divisible by 11.

%C Any term of the form a(11+n*12) appears to be divisible by 13.

%C Any term of the form a(1+n*22) appears to be divisible by 23.

%C Any term that is not prime appears to have its factors recurring periodically in the sequence as factors of higher terms.

%H Colin Barker, <a href="/A248877/b248877.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).

%F a(n) = 3*2^(n+3)-25 = A007283(n+3)-25.

%F a(n+1) = a(n)+3*2^(n+3) with a(1) = 23.

%F a(n) = 3*a(n-1)-2*a(n-2). - _Colin Barker_, Mar 05 2015

%F G.f.: x*(2*x+23) / ((x-1)*(2*x-1)). - _Colin Barker_, Mar 05 2015

%t Table[3*2^(n + 3) - 25, {n, 1, k}]

%t LinearRecurrence[{3,-2},{23,71},30] (* _Harvey P. Dale_, Apr 10 2021 *)

%o (PARI) Vec(x*(2*x+23)/((x-1)*(2*x-1)) + O(x^100)) \\ _Colin Barker_, Mar 05 2015

%o (Magma) [3*2^(n + 3) - 25: n in [1..30]]; // _Vincenzo Librandi_, Mar 08 2015

%K nonn,easy

%O 1,1

%A _Zeid Ghalyoun_, Mar 05 2015