A126430 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.

1, 3, 8, 14, 24, 36, 54, 73, 93, 119, 148, 179, 213, 254, 296, 339, 384, 431, 479, 531, 587, 645, 706, 769, 833, 899, 966, 1037, 1114, 1194, 1276, 1360, 1449, 1540, 1638, 1737, 1839, 1942, 2046, 2156, 2269, 2384, 2505, 2628, 2756, 2887, 3019, 3155, 3292, 3431

Offset: 1

Author

Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Mar 11 2007

Keywords

• nonn

Examples

			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.
		

Links

• David Consiglio, Jr., Table of n, a(n) for n = 1..1000

Programs

Python

keep = [1, 3]
for aa in range(50):
    flag = False
    temp = set()
    for x in keep:
        for y in keep:
            if x != y:
                temp.add(x+y)
                temp.add(abs(x-y))
            temp.add(x)
            temp.add(y)
    now = sorted(list(temp))
    for x in range(1, len(now)):
        if now[x] - now[x-1] != 1:
            keep.append(keep[-1]+now[x-1]+1)
            flag = True
            break
    if not flag:
        keep.append(keep[-1]+max(now)+1)
print(keep) # David Consiglio, Jr., Oct 09 2015

Extensions

More terms from David Consiglio, Jr., Oct 09 2015