A091857 Beginning with 1, (a(2n-1),a(2n)) = 1, (a(2n),a(2n+1))>1; a(n) is smallest value not yet used that makes this true.

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

Offset

1,2

Comments

It seems that for n>1, a(2n-1) 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. Adams-Watters, 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 !! (n-1)
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. Adams-Watters, Sep 01 2006

Data corrected for n > 52 by Reinhard Zumkeller, Feb 17 2015

Status

approved