A089781 Successive coprime numbers with distinct successive differences: gcd(a(k+1),a(k)) = gcd(a(m+1),a(m)) = 1 and a(k+1)-a(k) = a(m+1)-a(m) <==> m=k.

1, 2, 5, 7, 11, 16, 23, 29, 37, 46, 57, 67, 79, 92, 107, 121, 137, 154, 173, 191, 211, 232, 255, 277, 301, 326, 353, 379, 407, 436, 467, 497, 529, 562, 597, 631, 667, 704, 743, 781, 821, 862, 905, 947, 991, 1036, 1083, 1129, 1177, 1226, 1277

Offset: 1

Author

Amarnath Murthy, Nov 24 2003

Keywords

• nonn

Comments

Conjecture: If a(k+1)-a(k) = n then k < C*n. Can someone find an estimate for the constant C?

Examples

			5 follows 2 as 4 is not coprime to 2 and 5-2 = 3, 2-1 = 1.
		

Links

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

Crossrefs

Cf. A116966 (first differences), A111244.

Programs

Haskell

import Data.List (delete)
a089781 n = a089781_list !! (n-1)
a089781_list = 1 : f [1..] 1 where
   f xs y = g xs where
     g (z:zs) = if gcd y z == 1 then y' : f (delete z xs) y' else g zs
                where y' = y + z
-- Reinhard Zumkeller, Aug 15 2015

Formula

a(n+1) = a(n) + (smallest number coprime with a(n) and not already added). - Reinhard Zumkeller, Aug 15 2015

Extensions

More terms from Sean A. Irvine, Jun 01 2011