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

1,2

Links

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

Example

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.

Prog

(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

Crossrefs

Sequence in context: A062354 A257644 A135940 * A082474 A245181 A241563

Adjacent sequences: A126427 A126428 A126429 * A126431 A126432 A126433

Keyword

nonn

Author

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

Extensions

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

Status

approved