

A091857


Beginning with 1, (a(2n1),a(2n)) = 1, (a(2n),a(2n+1))>1; a(n) is smallest value not yet used that makes this true.


2



1, 2, 4, 3, 6, 5, 10, 7, 14, 9, 12, 11, 22, 13, 26, 15, 18, 17, 34, 19, 38, 21, 24, 23, 46, 25, 20, 27, 30, 29, 58, 31, 62, 33, 36, 35, 28, 37, 74, 39, 42, 41, 82, 43, 86, 45, 40, 47, 94, 49, 56, 51, 48, 53, 106, 55, 44, 57, 54, 59, 118, 61, 122, 63, 60, 67
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

It seems that for n>1, a(2n1) is always even, which forces a(2n) to be odd. Together, these prevent any further powers of 2 from appearing in the sequence. In fact, it appears that a(2n+1) is always either less than a(2n) or equal to a(2n) + the least prime factor of a(2n); and very rarely is a(2n) anything other than the smallest odd number not yet used (the first instance for n>1 is a(96) = 97 instead of 95).  Franklin T. AdamsWatters, Sep 01 2006


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


PROG

(Haskell)
import Data.List (delete)
a091857 n = a091857_list !! (n1)
a091857_list = 1 : f 1 1 [2..] where
f 1 z xs = g xs where
g (u:us) = if gcd u z == 1 then u : f 0 u (delete u xs) else g us
f 0 z xs = h xs where
h (v:vs) = if gcd v z /= 1 then v : f 1 v (delete v xs) else h vs
 Reinhard Zumkeller, Feb 17 2015


CROSSREFS

Cf. A091856.
Sequence in context: A179881 A227113 A034701 * A232642 A180625 A132340
Adjacent sequences: A091854 A091855 A091856 * A091858 A091859 A091860


KEYWORD

easy,nonn


AUTHOR

Amarnath Murthy, Mar 13 2004


EXTENSIONS

More terms from Franklin T. AdamsWatters, Sep 01 2006
Data corrected for n > 52 by Reinhard Zumkeller, Feb 17 2015


STATUS

approved



