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A026501 a(n) = least positive integer > a(n-1) and not a(j)*a(k) + a(k)*a(i) + a(i)*a(j) for 1<=i

%I A026501 #21 Aug 11 2015 20:42:59
%S A026501 1,2,3,4,5,6,7,8,9,10,12,13,15,16,18,21,22,24,25,28,30,33,37,40,42,45,
%T A026501 48,57,58,60,70,72,78,85,88,93,100,102,105,112,120,130,133,145,148,
%U A026501 165,168,177,190,210,217,221,232,240,253,254,262,263,267,273,277,280
%N A026501 a(n) = least positive integer > a(n-1) and not a(j)*a(k) + a(k)*a(i) + a(i)*a(j) for 1<=i<j<k<n.
%C A026501 Unlike A000926, this sequence is infinite. The first term not in A000926 is a(37) = 100. - _Ivan Neretin_, Jul 29 2015
%H A026501 Robert Israel, <a href="/A026501/b026501.txt">Table of n, a(n) for n = 1..4000</a>
%p A026501 N:= 1000: # to get all terms <= N
%p A026501 Allowed:= {$1..N}:
%p A026501 for count from 1 while Allowed <> {} do
%p A026501   a:= min(Allowed);
%p A026501   A[count]:= a;
%p A026501   Allowed:= Allowed minus{a, seq(seq(A[i]*A[j]+(A[i]+A[j])*a,j=1..i-1),i=1..count-1)};
%p A026501 od:
%p A026501 seq(A[i],i=1..count-1); # _Robert Israel_, Aug 11 2015
%o A026501 (PARI) oka(va, nv) = {for (i=1, nv, for (j=i+1, nv, for (k=j+1, nv, if (va[nv] == va[j]*va[k] + va[k]*va[i] + va[i]*va[j], return (0));););); return (1);}
%o A026501 finda(va) = {na = vecmax(va) + 1; va = concat(va, na); while(! oka(va, #va), va[#va] = na++); na;}
%o A026501 lista(nn) = {va = [1]; print1(1, ", "); for (n=1, nn, na = finda(va); print1(na, ", "); va = concat(va, na);); va;} \\ _Michel Marcus_, Aug 10 2015
%Y A026501 Cf. A000926.
%K A026501 nonn
%O A026501 1,2
%A A026501 _Clark Kimberling_
%E A026501 More terms from _Jud McCranie_