A255940 -id:A255940 - cp's OEIS frontend

A098551 Inverse of A098550.

1, 2, 3, 4, 9, 10, 15, 6, 5, 16, 22, 12, 23, 8, 7, 14, 30, 31, 43, 18, 17, 20, 51, 33, 11, 25, 19, 27, 61, 39, 62, 29, 24, 35, 13, 37, 79, 41, 21, 48, 87, 44, 88, 46, 26, 56, 101, 52, 40, 50, 28, 54, 114, 69, 34, 58, 47, 63, 127, 71, 132, 60, 42, 65, 36, 73, 142, 67, 49, 80, 153

Offset: 1

Reinhard Zumkeller, Sep 14 2004

nonn

Now known to be a permutation of the natural numbers: see the 2015 article by Applegate, Havermann, Selcoe, Shevelev, Sloane, and Zumkeller.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669 [math.NT], 2015.
Index entries for sequences that are permutations of the natural numbers

Cf. A098550, A098553.
Cf. A249943 (partial maxima).
Cf. A098479, A255940.

import Data.List (elemIndex); import Data.Maybe (fromJust)
a098551 = (+ 1) . fromJust . (`elemIndex` a098550_list)
-- Reinhard Zumkeller, Nov 21 2014

f[lst_List] := Block[{k = 4}, While[ GCD[ lst[[-2]], k] == 1 || GCD[ lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]]; Table[ Position[ Nest[ f, {1, 2, 3}, 120], n], {n, 71}] // Flatten (* Robert G. Wilson v, Nov 21 2014 *)

A098553(n) = a(a(n)).

A249167 a(n) = n if n <= 3, otherwise the smallest number not occurring earlier having at least one common Fermi-Dirac factor with a(n-2), but none with a(n-1).

Original entry on oeis.org

1, 2, 3, 8, 15, 4, 5, 12, 10, 21, 18, 7, 6, 28, 22, 20, 11, 24, 55, 14, 33, 26, 27, 13, 9, 39, 36, 30, 44, 32, 52, 16, 40, 48, 34, 57, 17, 19, 51, 38, 60, 46, 35, 23, 42, 92, 50, 64, 25, 56, 75, 58, 69, 29, 54, 116, 45, 68, 63, 76, 70, 100, 62, 84, 31, 66, 124, 74, 93, 37, 78, 148, 65, 72, 80

Offset: 1

Vladimir Shevelev, Dec 15 2014

nonn

Fermi-Dirac analog of A098550. Recall that every positive digit has a unique Fermi-Dirac representation as a product of distinct terms of A050376.
Conjecture: the sequence is a permutation of the positive integers.
Conjecture is true. The proof is similar to that for A098550 with minor changes. - Vladimir Shevelev, Jan 26 2015
It is interesting that while the first 10000 points (n, A098550(n)) lie on about 8 roughly straight lines, the first 10000 points (n,a(n)) here lie on only about 6 lines (cf. scatterplots of these sequences). - Vladimir Shevelev, Jan 26 2015

			a(4) is not 4, since 2 and 4 have no common Fermi-Dirac divisor; it is not 6, since a(3)=3 and 6 have the common divisor 3. So, a(4)=8, having the Fermi-Dirac representation 8=2*4.

Peter J. C. Moses, Table of n, a(n) for n = 1..10000
David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669, 2015 and J. Int. Seq. 18 (2015) 15.6.7..
Index entries for sequences that are permutations of the natural numbers

Cf. A098550, A050376.

Cf. A213925, A255940 (inverse).

import Data.List (delete, intersect)
a249167 n = a249167_list !! (n-1)
a249167_list = 1 : 2 : 3 : f 2 3 [4..] where
   f u v ws = g ws where
     g (x:xs) | null (intersect fdx $ a213925_row u) ||
                not (null $ intersect fdx $ a213925_row v) = g xs
              | otherwise =  x : f v x (delete x ws)
              where fdx = a213925_row x
-- Reinhard Zumkeller, Mar 11 2015

More terms from Peter J. C. Moses, Dec 15 2014

A255479 Inverse permutation to A255582.

Original entry on oeis.org

1, 2, 3, 4, 10, 5, 13, 6, 7, 8, 21, 9, 24, 11, 12, 16, 31, 14, 38, 18, 15, 23, 43, 20, 30, 22, 17, 25, 51, 28, 59, 27, 19, 29, 32, 37, 67, 36, 26, 34, 78, 35, 81, 39, 42, 41, 90, 44, 52, 46, 33, 48, 101, 47, 58, 50, 40, 49, 108, 55, 119, 57, 54, 64, 60, 63, 131, 66, 45, 62, 136, 68

Offset: 1

N. J. A. Sloane, Feb 27 2015

nonn

The differences |a(n)-A064664(n)| seem surprisingly small (see A255482).

About the definition: the map n -> A255582(n) is an element of the group of all permutations of the positive integers; this is the inverse of that permutation.

Cf. A098550, A255582, A064413, A064664, A255482.

Cf. A098551, A255940.

import Data.List (elemIndex); import Data.Maybe (fromJust)
a255479 = (+ 1) . fromJust. (`elemIndex` a255582_list)
-- Reinhard Zumkeller, Mar 10 2015

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A098551 Inverse of A098550.

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A249167 a(n) = n if n <= 3, otherwise the smallest number not occurring earlier having at least one common Fermi-Dirac factor with a(n-2), but none with a(n-1).

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A255479 Inverse permutation to A255582.

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