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

%I A066512 #9 Jun 09 2025 14:41:24
%S A066512 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,
%T A066512 71,74,77,80,83,86,89,94,97,103,106,109,115,118,121,126,129,135,138,
%U A066512 141,147,150,153,158,161,164,167,170,173,176,179,182,185,193,196,199
%N A066512 Least nonnegative integer not the sum or product of any previous pair. a(1)=0.
%H A066512 Michael S. Branicky, <a href="/A066512/b066512.txt">Table of n, a(n) for n = 1..10000</a>
%e A066512 a(13)=30, which is not a(i)+a(j) or a(i)*a(j) for any distinct i,j < 13.
%o A066512 (Python)
%o A066512 from itertools import count, islice
%o A066512 def agen(): # generator of terms
%o A066512     a, sums, products = [0], set(), set()
%o A066512     yield from a
%o A066512     for k in count(0):
%o A066512         if k not in sums and k not in products:
%o A066512             yield k
%o A066512             sums.update(k+a[i] for i in range(len(a)))
%o A066512             products.update(k*a[i] for i in range(len(a)))
%o A066512             a.append(k)
%o A066512         sums.discard(k)
%o A066512         products.discard(k)
%o A066512 print(list(islice(agen(), 61))) # _Michael S. Branicky_, Jun 09 2025
%Y A066512 Cf. A026416, A033627.
%K A066512 easy,nonn
%O A066512 1,4
%A A066512 _Brian Galebach_, Jan 04 2002