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A355547
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Numbers k such that x^2 - s*x + p has noninteger roots with s sum of digits of k and p product of digits of k.
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3
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1, 2, 3, 5, 6, 7, 8, 9, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 135, 136, 137, 138, 139, 141, 142, 144, 145, 147, 148, 149, 151, 152, 153, 154, 155, 156, 157, 159, 161, 162, 163, 165, 167, 168, 169, 171
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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k = 111 is a term, since the sum of the digits of 111 is 3, the product of the digits of 111 is 1 and the roots (3 - sqrt(5))/2 and (3 + sqrt(5))/2 of x^2 - 3*x + 1 are not integers.
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MATHEMATICA
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kmax=171; kdig:=IntegerDigits[k]; s:=Total[kdig]; p:=Product[Part[kdig, i], {i, Length[kdig]}]; a:={}; For[k=0, k<=kmax, k++, If[Not[Element[x/.Solve[x^2-s*x+p==0, x], Integers]], AppendTo[a, k]]]; a
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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