file1 contains multiple alphabetic sequences:
AETYUIOOILAKSJ
EAYEURIOPOSIDK
RYXURIAJSKDMAO
URITORIEJAHSJD
YWQIAKSJDHFKCM
HAJSUDIDSJSIAJ
AJDHDPFDIXSIBJ
JAQIAUXCNC
awk '(NR==FNR){a[$0]=substr($0,length);next}
{ for(key in a) if (a[key] == substr($0,key+0,1)) { print; break }
}' file2 file1
Here, the array a[key] is a associative array with the following key-value pairs:
key: value
3T T
10K K
... ...
When processing file2 with the line: (NR==FNR){a[$0]=substr($0,length);next}: we extract the value beforehand so we don't have to do it later on. The index is easily extracted with a math operation. Eg. "10K"+0=10 in Awk.
Processing file1 is done with the next line. Here we just check if the character matches for any of the entries in the associative array.