

A032858


Numbers whose base3 representation Sum_{i=0..m} d(i)*3^i has d(m) > d(m1) < d(m2) > ...


11



0, 1, 2, 3, 6, 7, 10, 11, 19, 20, 23, 30, 33, 34, 57, 60, 61, 69, 70, 91, 92, 100, 101, 104, 172, 173, 181, 182, 185, 208, 209, 212, 273, 276, 277, 300, 303, 304, 312, 313, 516, 519, 520, 543, 546, 547, 555, 556, 624, 627, 628, 636, 637
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OFFSET

1,3


COMMENTS

Every other base3 digit must be strictly less than its neighbors.  M. F. Hasler, Oct 05 2018
The terms can be generated in the following way: if A(n) are the terms with n digits in base 3, the terms with n+2 digits are obtained by prefixing them with '10' and with '20', and prefixing '21' to those starting with a digit '2'. It is easy to prove that #A(n) = A000045(n+2), since from the above we have #A(n+2) = 2*#A(n) + #A(n1) = #A(n) + #A(n+1). (The #A(n1) numbers starting with '2' are #A(n2) numbers prefixed with '20' and #A(n3) prefixed with '21'.)  M. F. Hasler, Oct 05 2018


LINKS

M. F. Hasler, Table of n, a(n) for n = 1..5000


FORMULA

a(A000071(n+3)) = floor(3^(n+1)/8) = A033113(n).  M. F. Hasler, Oct 05 2018


EXAMPLE

The base3 representation of the initial terms is 0, 1, 2, 10, 20, 21, 101, 102, 201, 202, 212, 1010, 1020, 1021, 2010, 2020, 2021, 2120, 2121, 10101, 10102, ...


MATHEMATICA

sdQ[n_]:=Module[{s=Sign[Differences[IntegerDigits[n, 3]]]}, s==PadRight[{}, Length[s], {1, 1}]]; Select[Range[0, 700], sdQ] (* Vincenzo Librandi, Oct 06 2018 *)


PROG

(PARI) is(n, b=3)=!for(i=2, #n=digits(n, b), (n[i1]n[i])*(1)^i>0return) \\ M. F. Hasler, Oct 05 2018


CROSSREFS

Cf. A032859 .. A032865 for base4 .. 10 variants.
Cf. A000975 (or A056830 in binary) for the base2 analog.
Cf. A306105 for these terms written in base 3.
Sequence in context: A026443 A204323 A278965 * A181498 A030703 A305927
Adjacent sequences: A032855 A032856 A032857 * A032859 A032860 A032861


KEYWORD

nonn,base


AUTHOR

Clark Kimberling


EXTENSIONS

Definition edited, crossreferences and a(1) = 0 inserted by M. F. Hasler, Oct 05 2018


STATUS

approved



