Re "Add the greatest whatever"

[N. J. A. Sloane]

The two sequences that Richard is referring to are
not quite in the database yet, but they soon will be.
Here they are:

%I A060984
%S A060984 1,2,3,4,8,12,21,37,73,137,258,514,998,1959,3895,7739
%N A060984 a(1) = 1; a(n+1) = a(n) + (largest square <= a(n)).
%C A060984 Arises in analyzing heap games.
%O A060984 1,2
%K A060984 nonn,easy,nice,more
%Y A060984 Cf. A060985.
%A A060984 Richard Guy (rkg at cpsc.ucalgary.ca), May 11 2001

%I A060985
%S A060985 1,2,3,6,12,22,43,79,157,310,610,1205,2381,4727,9383
%N A060985 a(1) = 1; a(n+1) = a(n) + (largest triangular number <= a(n)).
%C A060985 Arises in analyzing heap games.
%O A060985 1,2
%K A060985 nonn,easy,nice,more
%Y A060985 Cf. A060984.
%A A060985 Richard Guy (rkg at cpsc.ucalgary.ca), May 11 2001

njas