range = Range[4 10^6];
Position[Mod[10^5 NestList[Mod[ 10^6 #, 1355297] &, 10^6,Length[#] - 1] - (54 # + 46), 1355297], 0] &[range]
(* {{2331259}, {3776127}} *)

Compile`CompilerFunctions[] // Sort

fu = Compile[{{range, _Integer, 1}},Position[Mod[10^5 NestList[Mod[ 10^6    range, 1355297] &, 10^6,Length[range] - 1] - (54 range + 46), 1355297], 0]]
(*Compile::cset: Variable Compile`Variable$630 of type
{_Integer,0}    encountered in assignment of type {_Integer,1}. *)

Needs["CompiledFunctionTools`"]
CompilePrint[fu]