A033556 a(n+1) = 2a(n) - {largest prime < a(n)}.

3, 4, 5, 7, 9, 11, 15, 17, 21, 23, 27, 31, 33, 35, 39, 41, 45, 47, 51, 55, 57, 61, 63, 65, 69, 71, 75, 77, 81, 83, 87, 91, 93, 97, 105, 107, 111, 113, 117, 121, 129, 131, 135, 139, 141, 143, 147, 155, 159, 161, 165

Offset

0,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

a(n+1) = 2*a(n) - A151799(a(n)). - Reinhard Zumkeller, Jul 26 2012

Mathematica

a[n_] := a[n] = 2*a[n-1] - NextPrime[ a[n-1], -1]; a[0] = 3; Table[ a[n], {n, 0, 50}] (* Jean-François Alcover, Sep 24 2012 *)
NestList[2#-NextPrime[#, -1]&, 3, 50] (* Harvey P. Dale, Jul 19 2014 *)

Prog

(Haskell)
a033556 n = a033556_list !! n
a033556_list = iterate (\x -> 2*x - fromInteger (a151799 x)) 3
-- Reinhard Zumkeller, Jul 26 2012
(PARI) a(n) = if(n==0, 3, 2*a(n-1)-precprime(a(n-1)-1)) \\ Iain Fox, Oct 18 2017
(PARI) first(n) = my(res = vector(n)); res[1] = 3; for(i = 2, n, res[i] = 2 * res[i - 1] - precprime(res[i - 1] - 1)); res \\ David A. Corneth, Oct 18 2017

Crossrefs

Cf. A007917, A151799.

Sequence in context: A308168 A193339 A049646 * A219044 A032507 A325462

Adjacent sequences: A033553 A033554 A033555 * A033557 A033558 A033559

Keyword

nonn,easy,nice

Author

armand turpel (armand_t(AT)yahoo.com)

Status

approved