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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. 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(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

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Last modified January 15 08:51 EST 2021. Contains 340186 sequences. (Running on oeis4.)