Well, the first step to solving this problem is coming up with some more interesting fake data to play with, so the following __DATA__ segment contains 20 60 character strings with sequences of 4 numbers or more.

Script included so you can expand your data set if you so desire:

for (1..20) {
    my @str = map {int rand 10} (1..60);

    my $diff = join '', map {($str[$_] - $str[$_+1]) % 10} (0..$#str-1
+);
    
    redo unless $diff =~ /1{4}|9{4}/;

    print join('', @str) . "\n";
}

__DATA__
461771621368210983721913243963580233112903255149955120374576
412182871611285727937329810487417347645678899662426008558163
806445168622715729854145415356850576789033724164441981190358
737993205942843210944632043755783070487691419376068748520835
797836732611301651049157941402677493925908901268033467721123
800343673335834413425690063499636965547527671535789010360222
364556954738232740095412905428192849218058869868234154321153
656886016318465389850845261620694916565611559209695154321950
439823085483918818243602360632486757938483367890464586909210
275010825726438419734041987657085162773815821872771619322197
362862003186986435628956392997462270571538785287890111165953
865788969800483978909876396956896428059483834654443783640994
084943262444682256649196170826699756789404699917511813404654
038022435612197850835139478901471838789042407199858583654421
244712325541896615697820925442735727638540309574604984321042
799272593665633014792964321006295907297545039391442339309443
875134840933937552505069624569692178901372764210973501240868
160604373233208765433548554842941708483446447649679473623104
787966403724853567890040276258105492183424704761915858524942
234565329824361008677075492264130762647177370538202678949041

[download]
I verified that each of the above data sets all contain an absolute maximum. Here are the solutions: 
pos = 12, str = '21098'
pos = 37, str = '45678'
pos = 35, str = '67890'
pos = 13, str = '432109'
pos = 41, str = '89012'
pos = 48, str = '78901'
pos = 52, str = '54321'
pos = 52, str = '54321'
pos = 43, str = '67890'
pos = 24, str = '98765'
pos = 47, str = '78901'
pos = 19, str = '09876'
pos = 34, str = '56789'
pos = 25, str = '78901'
pos = 53, str = '43210'
pos = 23, str = '43210'
pos = 34, str = '78901'
pos = 14, str = '876543'
pos = 15, str = '567890'
pos =  0, str = '23456'

[download]

Update: Added expected results for fake data.

In reply to Re: Find Length Of Longest Ascending/Descending Sequence by wind
in thread Find Length Of Longest Ascending/Descending Sequence by Limbic~Region

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