A032917 Numbers having only digits 1 and 3 in their decimal representation.

1, 3, 11, 13, 31, 33, 111, 113, 131, 133, 311, 313, 331, 333, 1111, 1113, 1131, 1133, 1311, 1313, 1331, 1333, 3111, 3113, 3131, 3133, 3311, 3313, 3331, 3333, 11111, 11113, 11131, 11133, 11311, 11313, 11331, 11333, 13111, 13113

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

Numbers n such that product of digits of n is a power of 3. - Vincenzo Librandi Aug 19 2016

Links

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

Crossrefs

CF. A020451 (primes).

Programs

Magma

[n: n in [1..14000] | Set(IntegerToSequence(n, 10)) subset {1, 3}]; // Vincenzo Librandi, Jun 02 2012

Mathematica

Flatten[Table[FromDigits[#,10]&/@Tuples[{1,3},n],{n,5}]] (* Vincenzo Librandi, Jun 02 2012 *)

PARI

for(n=1, 5, p=2*vector(n, i, 10^(n-i))~; forvec(d=vector(n, i, [1, 3]/2), print1(d*p,","))) \\ M. F. Hasler, Mar 10 2014

Python

def a(n): return int(bin(n+1)[3:].replace('1', '3').replace('0', '1'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, May 13 2021

Python

def A032917(n): return (int(bin(m:=n+1)[3:])<<1) + (10**(m.bit_length()-1)-1)//9 # Chai Wah Wu, Oct 13 2023

Extensions

Definition reworded by M. F. Hasler, Mar 10 2014