A101369 -id:A101369 - cp's OEIS frontend

A101438 Inverse permutation to A101369.

1, 2, 3, 5, 7, 4, 9, 11, 6, 13, 15, 8, 17, 19, 21, 10, 23, 25, 12, 27, 29, 31, 14, 33, 35, 16, 37, 39, 41, 18, 43, 45, 20, 47, 49, 22, 51, 53, 55, 24, 57, 59, 26, 61, 63, 65, 28, 67, 69, 30, 71, 73, 32, 75, 77, 79, 34, 81, 83, 36, 85, 87, 89, 38, 91, 93, 40, 95, 97, 42, 99, 101

Offset: 1

Leroy Quet, Jan 18 2005

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

Cf. A101369.

import Data.List (elemIndex); import Data.Maybe (fromJust)
a101438 = (+ 1) . fromJust . (`elemIndex` a101369_list)
-- Reinhard Zumkeller, Jul 01 2013

More terms from David Wasserman, Mar 27 2008

A227113 Lexicographically earliest permutation of the natural numbers such that all pairs of even- and odd-indexed terms have a common divisor > 1.

Original entry on oeis.org

1, 2, 4, 3, 6, 5, 10, 7, 14, 8, 12, 9, 15, 11, 22, 13, 26, 16, 18, 17, 34, 19, 38, 20, 24, 21, 27, 23, 46, 25, 30, 28, 32, 29, 58, 31, 62, 33, 36, 35, 40, 37, 74, 39, 42, 41, 82, 43, 86, 44, 48, 45, 50, 47, 94, 49, 56, 51, 54, 52, 60, 53, 106, 55, 65, 57, 63

Offset: 1

Reinhard Zumkeller, Jul 01 2013

nonn

a(2*n) = smallest number not occurring earlier;
a(2*n+1) = smallest number having with a(2*n) a common divisor greater than 1 and not occurring earlier;
A227288(n) = gcd(a(n), a(n+1)).

			.   n | a(2n) a(2n+1) | GCD |         not occurring after step n
.  ---+---------------+-----+-------------------------------------------
.   0 |    _      1   |   _ |  {2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,..}
.   1 |    2      4   |   2 |  {3,5,6,7,8,9,10,11,12,13,14,15,16,17,..}
.   2 |    3      6   |   3 |  {5,7,8,9,10,11,12,13,14,15,16,17,18,19,..}
.   3 |    5     10   |   5 |  {7,8,9,11,12,13,14,15,16,17,18,19,20,..}
.   4 |    7     14   |   7 |  {8,9,11,12,13,15,16,17,18,19,20,21,22,..}
.   5 |    8     12   |   4 |  {9,11,13,15,16,17,18,19,20,21,22,23,24..}
.   6 |    9     15   |   3 |  {11,13,16,17,18,19,20,21,22,23,24,25,..}
.   7 |   11     22   |  11 |  {13,16,17,18,19,20,21,23,24,25,26,27,..}
.   8 |   13     26   |  11 |  {16,17,18,19,20,21,23,24,25,27,28,29,..}
.   9 |   16     18   |   2 |  {17,19,20,21,23,24,25,27,28,29,30,31,..} .

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

Cf. A227114 (inverse).

Cf. A101369, A184992.

import Data.List (delete)
a227113 n = a227113_list !! (n-1)
a227113_list = 1 : f [2..] where
   f (x:xs) = x : y : f (delete y xs)
     where y : _ = filter ((> 1) . (gcd x)) xs

Thanks to Zak Seidov (who suggested more elaboration) from Reinhard Zumkeller, Jul 05 2013

cp's OEIS Frontend

A101438 Inverse permutation to A101369.

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