A003596 Numbers of the form 2^i * 11^j.

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 121, 128, 176, 242, 256, 352, 484, 512, 704, 968, 1024, 1331, 1408, 1936, 2048, 2662, 2816, 3872, 4096, 5324, 5632, 7744, 8192, 10648, 11264, 14641, 15488, 16384, 21296, 22528, 29282, 30976, 32768

Offset

1,2

Comments

A204455(11*a(n)) = 11, and only for these numbers. - Wolfdieter Lang, Feb 04 2012

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 100 terms from Vincenzo Librandi)

Formula

The characteristic function of this sequence is given by Sum_{n >= 1} x^a(n) = Sum_{n >= 1} mu(22*n)*x^n/(1 - x^n), where mu(n) is the Möbius function A008683. Cf. with the formula of Hanna in A051037. - Peter Bala, Mar 18 2019

Sum_{n>=1} 1/a(n) = (2*11)/((2-1)*(11-1)) = 11/5. - Amiram Eldar, Sep 23 2020

a(n) ~ exp(sqrt(2*log(2)*log(11)*n)) / sqrt(22). - Vaclav Kotesovec, Sep 23 2020

Mathematica

fQ[n_] := PowerMod[22, n, n]==0; Select[Range[40000], fQ] (* Vincenzo Librandi, Feb 04 2012 *)

Prog

(PARI) list(lim)=my(v=List(), N); for(n=0, log(lim)\log(11), N=11^n; while(N<=lim, listput(v, N); N<<=1)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jun 28 2011
(Haskell)
import Data.Set (singleton, deleteFindMin, insert)
a003596 n = a003596_list !! (n-1)
a003596_list = f $ singleton (1, 0, 0) where
   f s = y : f (insert (2 * y, i + 1, j) $ insert (11 * y, i, j + 1) s')
         where ((y, i, j), s') = deleteFindMin s
-- Reinhard Zumkeller, May 15 2015
(Magma) [n: n in [1..2*10^5] | PrimeDivisors(n) subset [2, 11]]; // Vincenzo Librandi, Jun 27 2016
(GAP) Filtered([1..33000], n->PowerMod(22, n, n)=0); # Muniru A Asiru, Mar 19 2019

Crossrefs

Cf. A025612, A025616, A025621, A025625, A025629, A025632, A025634, A025635, A108761, A003597, A107988, A003598, A108698, A003599, A107788, A108687, A108779, A108090.

Sequence in context: A115797 A336627 A242313 * A018600 A018408 A018320

Adjacent sequences: A003593 A003594 A003595 * A003597 A003598 A003599

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved