A286812 - OEIS

%I #41 Sep 08 2022 08:46:19

%S 104,103,101,97,89,73,41,-23,-151,-407,-919,-1943,-3991,-8087,-16279,

%T -32663,-65431,-130967,-262039,-524183,-1048471,-2097047,-4194199,

%U -8388503,-16777111,-33554327,-67108759,-134217623,-268435351,-536870807,-1073741719,-2147483543

%N a(n) = 105 - 2^n.

%C Perhaps m = 105 is the largest number such that m - 2^n is prime for all 1 < n < log_2 m. Indeed 105 - 2^n is also prime for quite a few n > 6.7142455... For n = 9 we have 105 - 512 = -407 = (-1) * 11 * 37, the first instance of a composite term after a(0).

%H Erich Friedman, <a href="https://erich-friedman.github.io/numbers.html">What's Special About This Number?</a> Entry for 105.

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

%F G.f.: (104 - 209*x)/((1 - x)*(1 - 2*x)). - _Bruno Berselli_, May 22 2017

%t 105 - 2^Range[0, 31]

%o (PARI) vector(40, n, n--; 105-2^n) \\ _Bruno Berselli_, May 22 2017

%o (Python) [105-2**n for n in range(40)] # _Bruno Berselli_, May 22 2017

%o (Sage) [105-2^n for n in range(40)] # _Bruno Berselli_, May 22 2017

%o (Magma) [105-2^n: n in [0..40]]; // _Bruno Berselli_, May 22 2017

%Y Cf. A000079.

%K sign,easy

%O 0,1

%A _Alonso del Arte_, May 21 2017