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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
W. Sierpiński, Sur un problème concernant les nombres k * 2^n + 1, Elem. Math., 15 (1960), pp. 73-74.
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
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.)