A066512 Least nonnegative integer not the sum or product of any previous pair. a(1)=0.

0, 0, 1, 2, 4, 7, 10, 13, 16, 19, 22, 25, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 94, 97, 103, 106, 109, 115, 118, 121, 126, 129, 135, 138, 141, 147, 150, 153, 158, 161, 164, 167, 170, 173, 176, 179, 182, 185, 193, 196, 199

Offset: 1

Author

Brian Galebach, Jan 04 2002

Keywords

• easy
• nonn

Examples

			a(13)=30, which is not a(i)+a(j) or a(i)*a(j) for any distinct i,j < 13.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A026416, A033627.

Programs

Python

from itertools import count, islice
def agen(): # generator of terms
    a, sums, products = [0], set(), set()
    yield from a
    for k in count(0):
        if k not in sums and k not in products:
            yield k
            sums.update(k+a[i] for i in range(len(a)))
            products.update(k*a[i] for i in range(len(a)))
            a.append(k)
        sums.discard(k)
        products.discard(k)
print(list(islice(agen(), 61))) # Michael S. Branicky, Jun 09 2025