cp's OEIS Frontend

A101902 Numbers n that are not of the form ab+bc+cd+de+ea with 1<=a<=b<=c<=d<=e.

%I A101902 #8 Dec 14 2016 08:35:57
%S A101902 1,2,3,4,6,8,12,14,18,30,38,42,62
%N A101902 Numbers n that are not of the form ab+bc+cd+de+ea with 1<=a<=b<=c<=d<=e.
%C A101902 Conjecture that this sequence is complete. Note that, except for n=1 and n=2, n-1 is prime. The case of the 3-term binary form is treated in A025052. For the 4-term case, ab+bc+cd+da, no prime is representable because the 4 terms factor as (a+c)(b+d).
%C A101902 The sequence is indeed complete. Each sufficiently great number can be represented in one of the following ways:
%C A101902 n = 7k:     {1, 2, 5, 6, k - 6}
%C A101902 n = 7k + 1: {1, 1, 1, 6, k - 1}
%C A101902 n = 7k + 2: {1, 3, 3, 6, k - 4}
%C A101902 n = 7k + 3: {2, 3, 4, 5, k - 5}
%C A101902 n = 7k + 4: {1, 2, 2, 6, k - 2}
%C A101902 n = 7k + 5: {1, 2, 3, 6, k - 3}
%C A101902 n = 7k + 6: {1, 2, 4, 6, k - 4}
%C A101902 Smaller numbers can be checked individually. - _Ivan Neretin_, Dec 14 2016
%t A101902 nn=100; cnt5=Table[0, {nn}]; Do[n=a*b+b*c+c*d+d*e+e*a; If[n<=nn, cnt5[[n]]++ ], {a, nn}, {b, a, nn}, {c, b, nn}, {d, c, nn}, {e, d, nn}]; Flatten[Position[cnt5, 0]]
%Y A101902 Cf. A025052 (n not of form ab + bc + ca).
%K A101902 nonn,fini,full
%O A101902 1,2
%A A101902 _T. D. Noe_, Dec 20 2004
%E A101902 Definition corrected by _Ivan Neretin_, Dec 14 2016