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A167819
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Numbers with a distinct frequency for each ternary digit.
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4
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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
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Select[Range[168], Length[Union[DigitCount[ #, 3]]]==3&] [From Zak Seidov, Nov 13 2009]
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PROG
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(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", ")))
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CROSSREFS
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KEYWORD
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base,nonn,fini
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AUTHOR
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STATUS
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approved
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