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A340510 A permutation of the positive integers with a divisibility property (see Comments for precise definition). 1

%I

%S 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,

%T 44,17,47,49,19,52,20,55,57,22,60,62,24,65,25,68,70,27,73,75,29,78,30,

%U 81,83,32,86,33,89,91,35,94,96,37,99,38,102,104,40,107,109

%N A permutation of the positive integers with a divisibility property (see Comments for precise definition).

%C 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.

%H Alois P. Heinz, <a href="/A340510/b340510.txt">Table of n, a(n) for n = 1..10000</a>

%H Muharem Avdispahić and Faruk Zejnulahi, <a href="https://www.researchgate.net/publication/341726940_AN_INTEGER_SEQUENCE_WITH_A_DIVISIBILITY_PROPERTY">An integer sequence with a divisibility property</a>, Fibonacci Quarterly, Vol. 58:4 (2020), 321-333.

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

%t 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]]]]]];

%t Table[Print[n, " ", a[n]]; a[n], {n, 1, 100}] (* _Jean-François Alcover_, Jan 31 2021 *)

%Y Cf. A000045, A001622, A019444.

%K nonn,hear

%O 1,2

%A _N. J. A. Sloane_, Jan 28 2021

%E More terms from _Alois P. Heinz_, Jan 28 2021

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Last modified August 18 02:34 EDT 2022. Contains 356204 sequences. (Running on oeis4.)