cp's OEIS Frontend

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.

%I A089781 #17 Jan 11 2020 00:33:57
%S A089781 1,2,5,7,11,16,23,29,37,46,57,67,79,92,107,121,137,154,173,191,211,
%T A089781 232,255,277,301,326,353,379,407,436,467,497,529,562,597,631,667,704,
%U A089781 743,781,821,862,905,947,991,1036,1083,1129,1177,1226,1277
%N 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.
%C A089781 Conjecture: If a(k+1)-a(k) = n then k < C*n. Can someone find an estimate for the constant C?
%H A089781 Reinhard Zumkeller, <a href="/A089781/b089781.txt">Table of n, a(n) for n = 1..10000</a>
%F A089781 a(n+1) = a(n) + (smallest number coprime with a(n) and not already added). - _Reinhard Zumkeller_, Aug 15 2015
%e A089781 5 follows 2 as 4 is not coprime to 2 and 5-2 = 3, 2-1 = 1.
%o A089781 (Haskell)
%o A089781 import Data.List (delete)
%o A089781 a089781 n = a089781_list !! (n-1)
%o A089781 a089781_list = 1 : f [1..] 1 where
%o A089781    f xs y = g xs where
%o A089781      g (z:zs) = if gcd y z == 1 then y' : f (delete z xs) y' else g zs
%o A089781                 where y' = y + z
%o A089781 -- _Reinhard Zumkeller_, Aug 15 2015
%Y A089781 Cf. A116966 (first differences), A111244.
%K A089781 nonn
%O A089781 1,2
%A A089781 _Amarnath Murthy_, Nov 24 2003
%E A089781 More terms from _Sean A. Irvine_, Jun 01 2011