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, 13131, 13133, 13311, 13313, 13331, 13333

Offset

1,2

Links

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

Mathematica

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

Prog

(Magma) [n: n in [1..14000] | Set(IntegerToSequence(n, 10)) subset {1, 3}]; // 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

Crossrefs

Cf. A020451 (primes), A174813.

Sequence in context: A287348 A019374 A033680 * A006559 A023248 A386106

Adjacent sequences: A032914 A032915 A032916 * A032918 A032919 A032920

Keyword

nonn,base

Author

Clark Kimberling

Extensions

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

Incorrect comment removed by Jason Yuen, Dec 23 2025

Status

approved