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 A101902 Numbers n that are not of the form ab+bc+cd+de+ea with 1<=a<=b<=c<=d<=e. 0
 1, 2, 3, 4, 6, 8, 12, 14, 18, 30, 38, 42, 62 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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). The sequence is indeed complete. Each sufficiently great number can be represented in one of the following ways: n = 7k:     {1, 2, 5, 6, k - 6} n = 7k + 1: {1, 1, 1, 6, k - 1} n = 7k + 2: {1, 3, 3, 6, k - 4} n = 7k + 3: {2, 3, 4, 5, k - 5} n = 7k + 4: {1, 2, 2, 6, k - 2} n = 7k + 5: {1, 2, 3, 6, k - 3} n = 7k + 6: {1, 2, 4, 6, k - 4} Smaller numbers can be checked individually. - Ivan Neretin, Dec 14 2016 LINKS MATHEMATICA 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]] CROSSREFS Cf. A025052 (n not of form ab + bc + ca). Sequence in context: A029449 A028815 A014423 * A236912 A215966 A114312 Adjacent sequences:  A101899 A101900 A101901 * A101903 A101904 A101905 KEYWORD nonn,fini,full AUTHOR T. D. Noe, Dec 20 2004 EXTENSIONS Definition corrected by Ivan Neretin, Dec 14 2016 STATUS approved

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Last modified March 19 23:02 EDT 2019. Contains 321343 sequences. (Running on oeis4.)