Degrees of minimal polynomials that have a Salem number less than 1.3 as a zero.

8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 34, 36, 40, 44, 46

1

This is most likely a finite list. Boyd found most of the small Salem numbers.

T. D. Noe, Plot of 17 terms

David W. Boyd, Small Salem numbers, Duke Math. J. 44 (1977), no. 2, pp. 315-328.

Michael J. Mossinghoff, Small Salem Numbers

Chris Smyth, Salem numbers: a survey, arXiv 1408.0195 (Aug 01 2014)

Wikipedia, Salem number

nonn

T. D. Noe, Aug 06 2014