A032925 Numbers whose set of base-4 digits is a subset of {1,2}.

1, 2, 5, 6, 9, 10, 21, 22, 25, 26, 37, 38, 41, 42, 85, 86, 89, 90, 101, 102, 105, 106, 149, 150, 153, 154, 165, 166, 169, 170, 341, 342, 345, 346, 357, 358, 361, 362, 405, 406, 409, 410, 421, 422, 425, 426, 597, 598, 601, 602, 613, 614, 617, 618, 661, 662, 665

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Comments

Intersection of A023705 and A023717; A179888 is the intersection of this sequence and A053754. - Reinhard Zumkeller, Jul 31 2010

Links

• R. Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A023705, A023717, A179888, A053754.

Programs

C

#include 
uint32_t a_next(uint32_t a_n) {
    uint32_t t = (a_n + 0x55555556) ^ 0x55555555;
    return (a_n - t) & t;
} /* Falk Hüffner, Jan 22 2022 */

Haskell

import Data.List (transpose)
a032925 n = a032925_list !! (n-1)
a032925_list = 1 : 2 : (concat $ transpose [map (+ 1) fs, map (+ 2) fs])
               where fs = map (* 4) a032925_list
-- Reinhard Zumkeller, Apr 18 2015

Magma

[n: n in [1..1000] | Set(IntegerToSequence(n, 4)) subset {1, 2}]; // Vincenzo Librandi, Jun 05 2012

Maple

A032925 := proc(n)
    option remember;
    if n <= 2 then
        n;
    else
        if type(n,'even') then
            2+4*procname(n/2-1) ;
        else
            1+4*procname(floor(n/2)) ;
        end if;
    end if;
end proc:
seq(A032925(n),n=1..100) ;  # R. J. Mathar, Sep 07 2016

Mathematica

Flatten[Table[FromDigits[#,4]&/@Tuples[{1,2},n],{n,5}]] (* Vincenzo Librandi, Jun 05 2012 *)

Formula

a(2n) = 4a(n-1) + 2, a(2n+1) = 4a(n) + 1. - Ralf Stephan, Oct 07 2003, corrected by R. J. Mathar, Sep 07 2016