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

157115, 314229, 628457, 1256913, 2513825, 5027649, 10055297, 20110593, 40221185, 80442369, 160884737, 321769473, 643538945, 1287077889, 2574155777, 5148311553, 10296623105, 20593246209, 41186492417, 82372984833, 164745969665, 329491939329, 658983878657, 1317967757313

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., Vol. 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

E.g.f.: 78557*exp(2*x) + exp(x) - 78558. - Elmo R. Oliveira, Mar 10 2026

Mathematica

Table[1 + 78557 2^n, {n, 1, 25}] (* Vincenzo Librandi, May 19 2015 *)

Prog

(SageMath) [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, A258091 (smallest prime factors).

Sequence in context: A377949 A114658 A274364 * A245681 A278862 A250595

Adjacent sequences: A258070 A258071 A258072 * A258074 A258075 A258076

Keyword

nonn,easy

Author

Tom Edgar, May 18 2015

Status

approved