A167819 Numbers with a distinct frequency for each ternary digit.

9, 10, 12, 14, 16, 17, 18, 20, 22, 23, 24, 25, 27, 31, 37, 39, 41, 43, 49, 53, 54, 62, 67, 71, 74, 77, 78, 79, 81, 82, 84, 85, 90, 91, 93, 94, 108, 109, 111, 112, 117, 118, 120, 122, 124, 125, 130, 131, 133, 134, 148, 149, 151, 152, 157, 158, 160, 161, 162, 164, 168

Offset: 1

Author

Franklin T. Adams-Watters, Nov 13 2009

Keywords

• base
• nonn

Comments

The smallest number in the sequence that actually contains all 3 ternary digits is 248 = 100012_3. [Corrected by M. F. Hasler, Nov 02 2012]

The number 28 is in A031948 but not in this sequence A167819. This sequence is infinite, e.g. all powers 3^k, k>1 are member. Digit frequencies are [2,1,0] for the first 12 terms (with 3 digits in base 3, from 100[3] to 221[3]), then [3,1,0] for the next 16 terms with 4 digits in base 3 (from 1000[3] to 2221[3]), then [4,1,0] and [3,2,0] (5 digits in base 3, from 10000[3] to 22221[3]), followed by [5,1,0] or [4,2,0] or [3,2,1] (6 digits in base-3, from 10000[3] to 22221[3]), etc. - M. F. Hasler, Nov 02 2012

Examples

			9 = 100_3 is in the sequence, as it has 2 0's, 1 1, and 0 2's.
1 is not in the sequence, as it has the same number (0) of 0's and 2's.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A121977, A044951.

Programs

Mathematica

Select[Range[168],Length[Union[DigitCount[ #,3]]]==3&] (* Zak Seidov, Nov 13 2009 *)

PARI

/* In PARI versions < 2.6, define: digits(n,b=10)=local(r);r=[];while(n>0,r=concat([n%b],r);n\=b);r */
is_A167819(n)=local(d=digits(n,3),v=vector(3));for(k=1,#d,v[d[k]+1]++);#Set(v)==3
for(n=1,250,if(is_A167819(n),print1(n",")))