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A258073 a(n) = 1 + 78557*2^n. 4

%I

%S 157115,314229,628457,1256913,2513825,5027649,10055297,20110593,

%T 40221185,80442369,160884737,321769473,643538945,1287077889,

%U 2574155777,5148311553,10296623105,20593246209,41186492417,82372984833,164745969665,329491939329

%N a(n) = 1 + 78557*2^n.

%C 78557 is the (conjectured) smallest Sierpiński number (A076336). This means that every number in the current sequence is composite.

%C Every number in the sequence is divisible by some number in {3, 5, 7, 13, 19, 37, 73}.

%H Reinhard Zumkeller, <a href="/A258073/b258073.txt">Table of n, a(n) for n = 1..1000</a>

%H W. Sierpiński, <a href="http://dx.doi.org/10.5169/seals-20713">Sur un problème concernant les nombres k * 2^n + 1</a>, Elem. Math., 15 (1960), pp. 73-74.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Sierpinski_number">Sierpinski Number</a>

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

%F G.f.: x*(157115-157116*x)/((1-2*x)*(1-x)). - _Vincenzo Librandi_, May 19 2015

%F a(n) = 3*a(n-1)-2*a(n-2). - _Wesley Ivan Hurt_, Apr 26 2021

%t Table[1 + 78557 2^n, {n, 1, 25}] (* _Vincenzo Librandi_, May 19 2015 *)

%o (Sage) [78557*2^n+1 for n in [1..25]]

%o (MAGMA) [1+78557*2^n: n in [1..25]]; // _Vincenzo Librandi_ May 19 2015

%o (Haskell)

%o a258073 = (+ 1) . (* 78557) . (2 ^) -- _Reinhard Zumkeller_, May 19 2015

%Y Cf. A076336.

%Y Cf. A258091 (smallest prime factors).

%K nonn,easy

%O 1,1

%A _Tom Edgar_, May 18 2015

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Last modified July 23 12:19 EDT 2021. Contains 346259 sequences. (Running on oeis4.)