Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that f(n) - floor(f(n)) < 1/10^3.

Terms

a(0) =148a(1) =268a(2) =652a(3) =1194a(4) =1332a(5) =1519a(6) =2608a(7) =5650a(8) =5774a(9) =5868a(10) =6632a(11) =7260a(12) =9058a(13) =10153a(14) =10210a(15) =11076a(16) =12314a(17) =13049a(18) =13097a(19) =14370a(20) =15696a(21) =16170a(22) =18736a(23) =19571a(24) =21655a(25) =21814a(26) =22905a(27) =23325a(28) =24496a(29) =27435