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%I #17 Jul 12 2022 08:40:03
%S 1,2,3,5,6,7,8,9,111,112,113,114,115,116,117,118,119,121,123,124,125,
%T 126,127,128,129,131,132,133,135,136,137,138,139,141,142,144,145,147,
%U 148,149,151,152,153,154,155,156,157,159,161,162,163,165,167,168,169,171
%N 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.
%F a(n) ~ A052382(n) ~ n^k, where k = log(10)/log(9) = 1.04795.... - _Charles R Greathouse IV_, Jul 07 2022
%e 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.
%t 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
%Y Complement of A355497.
%Y Cf. A007953, A007954.
%Y Subsequence of A052382.
%K nonn,base
%O 1,2
%A _Stefano Spezia_ and _Jean-Marc Rebert_, Jul 06 2022
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