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 A258073 a(n) = 1 + 78557*2^n. 4
 157115, 314229, 628457, 1256913, 2513825, 5027649, 10055297, 20110593, 40221185, 80442369, 160884737, 321769473, 643538945, 1287077889, 2574155777, 5148311553, 10296623105, 20593246209, 41186492417, 82372984833, 164745969665, 329491939329 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 78557 is the (conjectured) smallest Sierpiński number (A076336). This means that every number in the current sequence is composite. Every number in the sequence is divisible by some number in {3, 5, 7, 13, 19, 37, 73}. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 W. Sierpiński, Sur un problème concernant les nombres k * 2^n + 1, Elem. Math., 15 (1960), pp. 73-74. Wikipedia, Sierpinski Number Index entries for linear recurrences with constant coefficients, signature (3,-2). FORMULA G.f.: x*(157115-157116*x)/((1-2*x)*(1-x)). - Vincenzo Librandi, May 19 2015 a(n) = 3*a(n-1)-2*a(n-2). - Wesley Ivan Hurt, Apr 26 2021 MATHEMATICA Table[1 + 78557 2^n, {n, 1, 25}] (* Vincenzo Librandi, May 19 2015 *) PROG (Sage) [78557*2^n+1 for n in [1..25]] (Magma) [1+78557*2^n: n in [1..25]]; // Vincenzo Librandi May 19 2015 (Haskell) a258073 = (+ 1) . (* 78557) . (2 ^) -- Reinhard Zumkeller, May 19 2015 CROSSREFS Cf. A076336. Cf. A258091 (smallest prime factors). Sequence in context: A297060 A114658 A274364 * A245681 A278862 A250595 Adjacent sequences: A258070 A258071 A258072 * A258074 A258075 A258076 KEYWORD nonn,easy AUTHOR Tom Edgar, May 18 2015 STATUS approved

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Last modified June 19 14:12 EDT 2024. Contains 373503 sequences. (Running on oeis4.)