

A249167


a(n) = n if n <= 3, otherwise the smallest number not occurring earlier having at least one common FermiDirac factor with a(n2), but none with a(n1).


6



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
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OFFSET

1,2


COMMENTS

FermiDirac analog of A098550. Recall that every positive digit has a unique FermiDirac 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


LINKS

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


EXAMPLE

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


PROG

(Haskell)
import Data.List (delete, intersect)
a249167 n = a249167_list !! (n1)
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


CROSSREFS

Cf. A098550, A050376.
Cf. A213925, A255940 (inverse).
Sequence in context: A076876 A124495 A007919 * A205101 A069752 A265694
Adjacent sequences: A249164 A249165 A249166 * A249168 A249169 A249170


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Dec 15 2014


EXTENSIONS

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


STATUS

approved



