OFFSET

1,2

COMMENTS

From Bernard Schott, Jun 30 2019: (Start)

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. 179-181.

LINKS

FORMULA

From Rémy Sigrist, Apr 05 2020: (Begin)

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

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

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

(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[n-1]+A[n-2]

else A[n]:= min(S)

fi;

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

od:

seq(A[i], i=1..N); # Robert Israel, Feb 07 2016

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

Reinhard Zumkeller, Dec 06 2004

STATUS

approved