A032810 Numbers using only digits 2 and 3.

2, 3, 22, 23, 32, 33, 222, 223, 232, 233, 322, 323, 332, 333, 2222, 2223, 2232, 2233, 2322, 2323, 2332, 2333, 3222, 3223, 3232, 3233, 3322, 3323, 3332, 3333, 22222, 22223, 22232, 22233, 22322, 22323, 22332, 22333, 23222, 23223

Offset

1,1

Comments

Identical to A007931 with substitution of digits 2 -> 3, 1 -> 2, i.e., application of the function A048379 or A256079(n) = n + A002275(A055642(n)). - M. F. Hasler, Mar 21 2015

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for 10-automatic sequences.

Formula

a(n) = f(n+1, 0) with f(n, x) = if n=1 then A004086(x) else f(floor(n/2), 10*x + 2 + n mod 2). - Reinhard Zumkeller, Sep 06 2008

a(n) is Theta(n^(log_2 10)); there are about n^(log_10 2) members of this sequence up to n. - Charles R Greathouse IV, Mar 18 2010

a(n) = A007931(n) + A002275(A000523(n+1)). A055642(a(n)) = A000523(n+1). - M. F. Hasler, Mar 21 2015

Mathematica

Flatten[Table[FromDigits[#, 10]&/@Tuples[{2, 3}, n], {n, 5}]] (* Vincenzo Librandi, May 27 2012 *)

Prog

(Magma) [n: n in [1..24000] | Set(Intseq(n)) subset {2, 3}]; // Vincenzo Librandi, May 27 2012
(Magma) [n eq 1 select 2 else IsOdd(n) select 10*Self(Floor(n/2))+2 else Self(n-1)+1: n in [1..40]]; // Bruno Berselli, May 27 2012
(Haskell)
a032810 = f 0 . (+ 1) where
   f y 1 = a004086 y
   f y x = f (10 * y + m + 2) x' where (x', m) = divMod x 2
-- Reinhard Zumkeller, Mar 18 2015
(PARI) A032810(n)=vector(#n=binary(n+1)[2..-1], i, 10^(#n-i))*n~+10^#n\9*2 \\ M. F. Hasler, Mar 26 2015
(Python)
def A032810(n): return int(bin(n+1)[3:])+(10**((n+1).bit_length()-1)-1<<1)//9 # Chai Wah Wu, Jul 15 2023

Crossrefs

Cf. A020458, A143967, A248907 (permutation).

Cf. A032804-A032816 (in other bases), A007088 (digits 0 & 1), A007931 (digits 1 & 2), A032834 (digits 3 & 4), A256290 (digits 4 & 5), A256291 (digits 5 & 6), A256292 (digits 6 & 7), A256340 (digits 7 & 8), A256341 (digits 8 & 9).

Sequence in context: A084797 A163902 A154865 * A248907 A062921 A298470

Adjacent sequences: A032807 A032808 A032809 * A032811 A032812 A032813

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved