SMA Y HAD LTSS FROM ACR X IN TCA ATA. SYS ERROR.

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ACR X CLRED FOR TKOF BEHIND A LIGHT JET TRANSPORT. TO BE EXTRA SAFE AND CONTRIBUTE TO PAX COMFORT I CLBED THE ACFT STEEPLY TO AVOID ANY POSSIBLE WAKE TURB. WE CLBED ABOVE THE JET'S DEP PATH. AT 800 FT THE FO SAW SMA Y; A SINGLE ENG ACFT; AT OUR 10 O'CLOCK AT APPROX 1000 FT MSL AND APPROX 2000 FT HORIZ. I SAW IT THEN FOR THE FIRST TIME BUT DETERMINED THAT THERE WAS NO CONFLICT BTWN OUR 2 ACFT AND CONTINUED THE CLB. THE REASON WHY THERE WAS NO CONFLICT WAS BECAUSE JUST PRIOR TO THE FO POINTING OUT THE TFC I HAD BEGUN REDUCING OUR CLB ANGLE IN ORDER TO ACCELERATE TO CRUISE SPD. HAD I MAINTAINED THE STEEP CLB OUR ACFT WOULD HAVE HAD A HORIZ SEPARATION OF ROUGHLY 500 FT AT A COMMON ALT. OTHER CONTRIBUTING FACTORS FOR THE GREATER SEPARATION WAS THE SLOW SPD OF SMA Y; THE SMA'S LNDG LIGHT WHICH MADE IT EASIER TO SPOT AND THE ALERTNESS OF THE FO. THE TWR DID NOT ADVISE US IN THE TKOF CLRNC OR AT ANY OTHER TIME OF THIS TFC. SUPPLEMENTAL INFO FROM ACN 197963. AFTER TKOF IN OUR CLB FROM SEATT;E RWY 16L; WE SAW SMA Y AT 10 O'CLOCK AND APPROX 1000 FT AWAY. WE WERE READY TO TAKE EVASIVE ACTION; BUT SMA Y'S SPD WAS SLOW ENOUGH THAT WE DIDN'T NEED TO. WE FIRST SAW TFC WHEN WE WERE APPROX 800 FT AGL AND HE LOOKED TO BE 900-1000 FT AGL. WE NOTIFIED TWR AFTER CONFLICT RESOLUTION THAT WE HAD SMA Y TFC IN SIGHT AT 10 O'CLOCK. TWR SAID THAT THEY THOUGHT THEY HAD TOLD US ABOUT THE SMA Y TFC; WHICH THEY HAD NOT. THE TWR APOLOGIZED. THE PROBLEM WITH THIS OVERSIGHT; IS THAT HAD THE TFC BEEN FASTER; A POSSIBLE MIDAIR COULD HAVE OCCURRED.