There's no way using RegEx that I know of, but here is a naive functional approach.
First, loop through the string and compare each character against the next two characters by adding +1 and +2 to the current index and comparing appropriately.
Second, loop through the string again and compare checks the next two characters against the current character to see if they are sequential.
If both loops fail to find sequential characters, the function returns true, otherwise it returns false.
The first four return false (fail), while the last three return true (pass).
function test(s) {
// Check for sequential numerical characters
for(var i in s)
if (+s[+i+1] == +s[i]+1 &&
+s[+i+2] == +s[i]+2) return false;
// Check for sequential alphabetical characters
for(var i in s)
if (String.fromCharCode(s.charCodeAt(i)+1) == s[+i+1] &&
String.fromCharCode(s.charCodeAt(i)+2) == s[+i+2]) return false;
return true;
}
// For demo purposes only
var tests = [
'efg123!$',
'abcd567%',
'xyz789^&',
'#hijk23456',
'ryiiu562@',
'erty745#',
'gjnfl45566^'
], sep = 'u2192 ', out = ['Fail','Pass'], eol = '<br>';
document.write('<pre>');
for(var i in tests) document.write(tests[i] + sep + out[+test(tests[i])] + eol);
document.write('</pre>');
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