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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). 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified August 17 21:16 EDT 2018. Contains 313817 sequences. (Running on oeis4.)