hello I am trying to make a memory from scratch

I am encountering two problems that maybe someone in the list could resolve.

First, my memory object only allows list of numbers,
 because I am triggering [list] and the cold inlet only allows list of numbers
I just don't undrstand why.

Second, I would like to find a way to ignore redondant entries of memory index.

memory.pd

#N canvas 0 0 578 582 10;
#X obj 9 12 inlet;
#X msg 129 299 \, 1 cat \, 2 cat dog \, 3 test \, 4 5 6 7;
#X msg 214 211 addcomma;
#X obj 129 140 pp add2;
#X msg 183 211 set;
#X obj 181 139 spigot 1;
#X msg 214 110 0;
#X obj 130 108 t b a b b b;
#X msg 245 111 1;
#X obj 245 88 r \$1-init;
#X obj 201 427 ==;
#X obj 158 447 spigot;
#X obj 158 468 outlet;
#X obj 292 216 inlet;
#X obj 129 324 list split 1;
#X obj 314 47 route clear;
#X obj 339 171 bng 15 250 50 0 empty empty empty 0 -6 0 8 -262144 -1
-1;
#X obj 284 252 t b b b a;
#X obj 200 396 f;
#X obj 154 422 list;
#X connect 0 0 7 0;
#X connect 0 0 15 0;
#X connect 1 0 14 0;
#X connect 2 0 1 0;
#X connect 3 0 1 0;
#X connect 4 0 1 0;
#X connect 5 0 4 0;
#X connect 6 0 5 1;
#X connect 7 1 3 0;
#X connect 7 2 6 0;
#X connect 7 3 5 0;
#X connect 7 4 2 0;
#X connect 8 0 5 1;
#X connect 9 0 8 0;
#X connect 10 0 11 1;
#X connect 11 0 12 0;
#X connect 13 0 17 0;
#X connect 14 0 18 1;
#X connect 14 1 19 1;
#X connect 15 0 16 0;
#X connect 16 0 4 0;
#X connect 17 0 19 0;
#X connect 17 1 18 0;
#X connect 17 2 1 0;
#X connect 17 3 10 1;
#X connect 18 0 10 0;
#X connect 19 0 11 0;

memory-test.pd

#N canvas 0 0 454 304 10;
#X obj 215 189 memory;
#X msg 149 63 1 cat;
#X msg 189 62 2 cat dog;
#X msg 126 37 3 test;
#X msg 105 14 4 5 6 7;
#X msg 390 105 1;
#X msg 400 130 2;
#X floatatom 404 62 5 0 0 0 - - -;
#X msg 266 57 clear;
#X obj 221 231 print mem;
#X msg 389 168 3;
#X msg 391 209 4;
#X connect 0 0 9 0;
#X connect 1 0 0 0;
#X connect 2 0 0 0;
#X connect 3 0 0 0;
#X connect 4 0 0 0;
#X connect 5 0 0 1;
#X connect 6 0 0 1;
#X connect 7 0 0 1;
#X connect 8 0 0 0;
#X connect 10 0 0 1;
#X connect 11 0 0 1;



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