A355547 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.

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

Offset

1,2

Links

Table of n, a(n) for n=1..56.

Formula

a(n) ~ A052382(n) ~ n^k, where k = log(10)/log(9) = 1.04795.... - Charles R Greathouse IV, Jul 07 2022

Example

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.

Mathematica

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

Crossrefs

Complement of A355497.

Cf. A007953, A007954.

Subsequence of A052382.

Sequence in context: A244217 A351224 A039122 * A031975 A028729 A213367

Adjacent sequences: A355544 A355545 A355546 * A355548 A355549 A355550

Keyword

nonn,base

Author

Stefano Spezia and Jean-Marc Rebert, Jul 06 2022

Status

approved