A167819 - OEIS

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

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OFFSET

1,1

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

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

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.

MATHEMATICA

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

PROG

(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", ")))

CROSSREFS