%I #18 Jan 27 2025 16:50:56
%S 1,3,8,14,24,36,54,73,93,119,148,179,213,254,296,339,384,431,479,531,
%T 587,645,706,769,833,899,966,1037,1114,1194,1276,1360,1449,1540,1638,
%U 1737,1839,1942,2046,2156,2269,2384,2505,2628,2756,2887,3019,3155,3292,3431
%N a(n)-a(n-1) is the smallest integer missing in the auxiliary set composed of the previous terms and sums and differences of previous pairs of the sequence.
%H David Consiglio, Jr., <a href="/A126430/b126430.txt">Table of n, a(n) for n = 1..1000</a>
%e a(3)-a(2) = 5 because 1 = a(1), 2 = a(2)-a(1), 3 = a(2), 4 = a(1)+a(2) = maximum of the auxiliary set.
%o (Python)
%o keep = [1, 3]
%o for aa in range(50):
%o flag = False
%o temp = set()
%o for x in keep:
%o for y in keep:
%o if x != y:
%o temp.add(x+y)
%o temp.add(abs(x-y))
%o temp.add(x)
%o temp.add(y)
%o now = sorted(list(temp))
%o for x in range(1, len(now)):
%o if now[x] - now[x-1] != 1:
%o keep.append(keep[-1]+now[x-1]+1)
%o flag = True
%o break
%o if not flag:
%o keep.append(keep[-1]+max(now)+1)
%o print(keep) # _David Consiglio, Jr._, Oct 09 2015
%K nonn
%O 1,2
%A Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Mar 11 2007
%E More terms from _David Consiglio, Jr._, Oct 09 2015