A075388 -id:A075388 - cp's OEIS frontend

A075383 Rearrangement of natural numbers so that next n numbers are each divisible by n.

1, 2, 4, 3, 6, 9, 8, 12, 16, 20, 5, 10, 15, 25, 30, 18, 24, 36, 42, 48, 54, 7, 14, 21, 28, 35, 49, 56, 32, 40, 64, 72, 80, 88, 96, 104, 27, 45, 63, 81, 90, 99, 108, 117, 126, 50, 60, 70, 100, 110, 120, 130, 140, 150, 160, 11, 22, 33, 44, 55, 66, 77, 121, 132, 143, 154, 84

Offset: 1

Amarnath Murthy, Sep 22 2002

Integer permutation with inverse A096780: a(A096780(n))=A096780(a(n))=n; A096781(n) = a(a(n)). - Reinhard Zumkeller, Jul 09 2004
Primes occur in natural order: a(A072205(n)) = A000040(n). - Reinhard Zumkeller, Jun 22 2009
n = greatest common divisor of row n. - Reinhard Zumkeller, Nov 30 2015

			   1;
   2,  4;
   3,  6,  9;
   8, 12, 16, 20;
   5, 10, 15, 25, 30;
  18, 24, 36, 42, 48, 54;
   7, 14, 21, 28, 35, 49, 56;
  32, ...

R. Zumkeller, Table of n, a(n) for n = 1..10000 - _Reinhard Zumkeller_, Jun 22 2009
Index entries for sequences that are permutations of the natural numbers

Cf. A075384, A075385, A075386, A075387, A075388, A075389, A075390.

Cf. A000040, A072205, A096780, A096781, A263896 (central terms).

import Data.List ((\\))
a075383 n k = a075383_tabl !! (n-1) !! (k-1)
a075383_row n = a075383_tabl !! (n-1)
a075383_tabl = f 1 [1..] where
   f x zs = ys : f (x + 1) (zs \\ ys) where
            ys = take x $ filter ((== 0) . (`mod` x)) zs
a075383_list = concat a075383_tabl
-- Reinhard Zumkeller, Nov 30 2015

row[1] = {1}; row[n_] := row[n] = (For[rows = Join[row /@ Range[n-1]]; ro = {}; k = n, Length[ro] < n, k = k+n, If[FreeQ[rows, k], AppendTo[ro, k]]]; ro); Array[row, 12] // Flatten (* Jean-François Alcover, Apr 28 2017 *)

More terms from Sascha Kurz, Jan 28 2003

A075384 Initial term of n-th group in A075383.

Original entry on oeis.org

1, 2, 3, 8, 5, 18, 7, 32, 27, 50, 11, 84, 13, 98, 75, 128, 17, 162, 19, 200, 147, 242, 23, 312, 125, 338, 243, 392, 29, 510, 31, 512, 363, 578, 245, 684, 37, 722, 507, 920, 41, 882, 43, 968, 765, 1058, 47, 1392, 343, 1250, 867, 1352, 53, 1458, 605, 1624, 1083, 1682, 59, 2220, 61, 1922, 1449, 2368, 845

Offset: 1

Amarnath Murthy, Sep 22 2002

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Cf. A075383, A075385, A075386, A075387, A075388.

a075384 = head . a075383_row  -- Reinhard Zumkeller, Nov 29 2015

A075383 := proc(nmax) local a,n,ct,k; a := [1,2,4] ; for n from 3 do ct := 0 ; for k from 1 do if (k*n) in a then ; else a := [op(a),k*n] ; ct := ct+1 ; if ct >= n then break ; fi ; fi; od: if nops(a) > nmax then RETURN(a) ; fi; od: end: A075384 := proc(n,a075383) local i,k ; i := 1 ; for k from 1 to n-1 do i := i+k ; if i > nops(a075383) then RETURN(-1) ; fi; od: RETURN(op(i,a075383)) ; end: a075383 := A075383(4000) : for n from 1 to 70 do a084 := A075384(n,a075383) ; if a084 < 0 then break; else printf("%d,",a084) ; fi; od:

row[n_] := row[n] = If[n == 1, {1}, rows = Join[row /@ Range[n-1]]; ro = {}; For[k = n, Length[ro] < n, k = k + n, If[FreeQ[rows, k], AppendTo[ro, k]]]; ro]; a[n_] := row[n][[1]]; Array[a, 65] (* Jean-François Alcover, Jan 27 2018 *)

More terms from Reinhard Zumkeller, Jul 09 2004

Removed claim on relation to A096776. Corrected from a(20) on by R. J. Mathar, Oct 31 2008

cp's OEIS Frontend

A075383 Rearrangement of natural numbers so that next n numbers are each divisible by n.

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