A102487 Numbers in base-12 representation that can be written with decimal digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 84, 85, 86

Offset: 1

Author

Reinhard Zumkeller, Jan 12 2005

Keywords

• nonn
• base

Comments

Numbers that are only in this sequence or only in A039274 but not in both are n= 131, 142, 275, 286, 419, 430 etc: see A039558. [From R. J. Mathar, Aug 30 2008]

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Duodecimal
• Wikipedia, Duodecimal

Crossrefs

Complement of A102488; A102489, A102491, A102493.

Cf. A033048 (subsequence).

Programs

Haskell

import Data.List (unfoldr)
a102487 n = a102487_list !! (n-1)
a102487_list = filter (all (< 10) . unfoldr (\x ->
   if x == 0 then Nothing else Just $ swap $ divMod x 12)) [0..]
-- Reinhard Zumkeller, Apr 18 2011

Mathematica

fQ[n_] := Last@ Union@ IntegerDigits[n, 12] < 10; Select[ Range[0, 86], fQ] (* Robert G. Wilson v, Apr 17 2012 *)

PARI

{for(testn=0,87,
lgt=1;
for(i=1,1000,if(12^i > testn,lgt=i;break()));
atst=testn;pasr=1;
for(j=1,lgt,lasd=atst%12;
if(lasd<10,atst=(atst-lasd)/12,pasr=0;break()));
if(pasr==1,print1(testn,", ")))}
\\ Douglas Latimer, Apr 17 2012

Python

A102487_list = [int(str(x), 12) for x in range(10**6)] # Chai Wah Wu, Apr 09 2016