

A101544


Smallest permutation of the natural numbers with a(3*k2) + a(3*k1) = a(3*k), k > 0.


8



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, 43, 24, 25, 49, 26, 27, 53, 28, 30, 58, 31, 32, 63, 34, 35, 69, 36, 37, 73, 38, 40, 78, 41, 42, 83, 44, 45, 89, 46, 47, 93, 48, 50, 98, 51, 52, 103, 54, 55, 109, 56, 57, 113, 59, 60
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OFFSET

1,2


COMMENTS

Inverse: a101545; a101546(n) = a(a(n)).
The terms can also be written simply following this array with 3 columns:
1st column 2nd column 3rd column
1 + 2 = 3
4 + 5 = 9
6 + 7 = 13
8 + 10 = 18
11 + 12 = 23
14 + 15 = 29
16 + 17 = 33
... ... ...
Question: in which column ends up the repdigit R_m(d) with m times the digit d?
Answer: R_m(d) will be in:
1) column 1 if d = 1, 4, 6, 8, or if d = 9 and m is even;
2) column 2 if d = 2, 5, 7;
3) column 3 if d = 3, or if d = 9 and m is odd.
Problem coming from Kruzemeyer et al. (End)


REFERENCES

Mark I. Krusemeyer, George T. Gilbert, Loren C. Larson, A Mathematical Orchard, Problems and Solutions, MAA, 2012, Problem 99, pp. 179181.


LINKS



FORMULA

(End)


MAPLE

N:= 100: # to get a(1) .. a(N)
S:= {$1..N}:
for n from 1 to N do
if n mod 3 = 0 then A[n] := A[n1]+A[n2]
else A[n]:= min(S)
fi;
S:= S minus {A[n]};
od:


MATHEMATICA

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 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



