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 A101544 Smallest permutation of the natural numbers with a(3*k-2) + a(3*k-1) = a(3*k), k > 0. 7

%I

%S 1,2,3,4,5,9,6,7,13,8,10,18,11,12,23,14,15,29,16,17,33,19,20,39,21,22,

%T 43,24,25,49,26,27,53,28,30,58,31,32,63,34,35,69,36,37,73,38,40,78,41,

%U 42,83,44,45,89,46,47,93,48,50,98,51,52,103,54,55,109,56,57,113,59,60

%N Smallest permutation of the natural numbers with a(3*k-2) + a(3*k-1) = a(3*k), k > 0.

%C Inverse: a101545; a101546(n) = a(a(n)).

%C From _Bernard Schott_, Jun 30 2019: (Start)

%C The terms can also be written simply following this array with 3 columns:

%C 1st column 2nd column 3rd column

%C 1 + 2 = 3

%C 4 + 5 = 9

%C 6 + 7 = 13

%C 8 + 10 = 18

%C 11 + 12 = 23

%C 14 + 15 = 29

%C 16 + 17 = 33

%C ... ... ...

%C Question: in which column ends up the repdigit R_m(d) with m times the digit d?

%C Answer: R_m(d) will be in:

%C 1) column 1 if d = 1, 4, 6, 8, or if d = 9 and m is even;

%C 2) column 2 if d = 2, 5, 7;

%C 3) column 3 if d = 3, or if d = 9 and m is odd.

%C Problem coming from Kruzemeyer et al. (End)

%D Mark I. Krusemeyer, George T. Gilbert, Loren C. Larson, A Mathematical Orchard, Problems and Solutions, MAA, 2012, Problem 99, pp. 179-181.

%H Ivan Neretin, <a href="/A101544/b101544.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F From _Rémy Sigrist_, Apr 05 2020: (Begin)

%F - a(3*n-2) = A249031(2*n-1),

%F - a(3*n-1) = A249031(2*n),

%F - a(3*n) = A075326(n).

%F (End)

%p N:= 100: # to get a(1) .. a(N)

%p S:= {\$1..N}:

%p for n from 1 to N do

%p if n mod 3 = 0 then A[n] := A[n-1]+A[n-2]

%p else A[n]:= min(S)

%p fi;

%p S:= S minus {A[n]};

%p od:

%p seq(A[i],i=1..N); # _Robert Israel_, Feb 07 2016

%t Fold[Append[#1, If[Divisible[#2, 3], #1[[-1]] + #1[[-2]], Min@Complement[Range[Max@#1 + 1], #1]]] &, {1}, Range[2, 71]] (* _Ivan Neretin_, Feb 05 2016 *)

%Y Cf. A075326, A249031.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Dec 06 2004

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Last modified June 20 06:56 EDT 2021. Contains 345157 sequences. (Running on oeis4.)