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A340510 A permutation of the positive integers with a divisibility property (see Comments for precise definition). 1
1, 3, 5, 2, 8, 10, 4, 13, 15, 6, 18, 7, 21, 23, 9, 26, 28, 11, 31, 12, 34, 36, 14, 39, 41, 16, 44, 17, 47, 49, 19, 52, 20, 55, 57, 22, 60, 62, 24, 65, 25, 68, 70, 27, 73, 75, 29, 78, 30, 81, 83, 32, 86, 33, 89, 91, 35, 94, 96, 37, 99, 38, 102, 104, 40, 107, 109 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(1)=1; thereafter a(n) is the least positive number not yet in the sequence such that Sum_{i=1..n} a(i) == 1 mod n+1.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Muharem Avdispahić and Faruk Zejnulahi, An integer sequence with a divisibility property, Fibonacci Quarterly, Vol. 58:4 (2020), 321-333.

FORMULA

Theorem 1 of Avdispahić and Zejnulahi gives an explicit formula involving Fibonacci numbers.

MATHEMATICA

a[n_] := a[n] = Switch[n, 1, 1, 2, 3, 3, 5, 4, 2, _, Module[{aa, ss, dd, an}, aa = Array[a, n-1]; ss = Sort[aa]; dd = Differences[ss]; For[an = Select[Transpose[{Rest[ss], dd}], #[[2]] == 1 &][[-1, 1]]+1, True, an++, If[FreeQ[aa = Array[a, n-1], an], If[Mod[Total[aa] + an, n+1] == 1, Return[an]]]]]];

Table[Print[n, " ", a[n]]; a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 31 2021 *)

CROSSREFS

Cf. A000045, A001622, A019444.

Sequence in context: A282348 A026193 A026143 * A075626 A152649 A327263

Adjacent sequences:  A340507 A340508 A340509 * A340511 A340512 A340513

KEYWORD

nonn,hear

AUTHOR

N. J. A. Sloane, Jan 28 2021

EXTENSIONS

More terms from Alois P. Heinz, Jan 28 2021

STATUS

approved

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Last modified June 30 06:00 EDT 2022. Contains 354914 sequences. (Running on oeis4.)