OFFSET
1,2
COMMENTS
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
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..
EXAMPLE
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.
PROG
(Haskell)
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Dec 15 2014
EXTENSIONS
More terms from Peter J. C. Moses, Dec 15 2014
STATUS
approved