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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. 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Inverse: a101545; a101546(n) = a(a(n)). 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 Ivan Neretin, Table of n, a(n) for n = 1..10000 Index entries for sequences that are permutations of the natural numbers 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 Cf. A075326, A249031. Sequence in context: A105950 A227778 A166276 * A171100 A240062 A255129 Adjacent sequences: A101541 A101542 A101543 * A101545 A101546 A101547 KEYWORD nonn AUTHOR Reinhard Zumkeller, Dec 06 2004 STATUS approved

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Last modified September 23 05:21 EDT 2023. Contains 365532 sequences. (Running on oeis4.)