A121977 -id:A121977 - cp's OEIS frontend

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

Franklin T. Adams-Watters, Nov 13 2009

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

			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.

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

Cf. A121977, A044951.

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

/* 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",")))

cp's OEIS Frontend

A167819 Numbers with a distinct frequency for each ternary digit.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI