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

Offset: 1

Author

Tom Edgar, May 18 2015

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A076336.

Cf. A258091 (smallest prime factors).

Programs

Haskell

a258073 = (+ 1) . (* 78557) . (2 ^)  -- Reinhard Zumkeller, May 19 2015

Magma

[1+78557*2^n: n in [1..25]]; // Vincenzo Librandi May 19 2015

Mathematica

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

Sage

[78557*2^n+1 for n in [1..25]]

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