Case insensitive version of strstr()

In order to solve a problem from K&R C book, I am trying to write a function strstrci() which is the case insensitive version of strstr()

char * strstrci (char *s, char *p)
{
    int i, j;
    for (i = 0; *(s + i) != '\0'; i++)
    {
        if (*(s + i) == *p || *(s + i) == *p + 32 || *(s + i) == *p - 32)
        {
            for (j = 1; *(s + i + j) == *(p + j) || *(s + i + j) == *(p + j) + 32 || *(s + i + j) == *(p + j) - 32; j++)
            {
                if (*(p + j) == '\0')
                    return (s + i);
            }
        }
    }
    return NULL;
}

The function seems to work well for all cases except when the pattern is the last part of the input string. For example: string : On a wall he sat pattern: sat In such a case it returns a NULL. Please point out the mistake

Solution

There are multiple problems:

The arguments should be typed const char *.
Empty strings should be handled in a way consistent with strstr: an empty string pointed to by p should be found at the beginning of s, even if s points to an empty string.
The offset 32 is ASCII specific, which may be OK, but it is not correct for all characters. Your function will erroneously match @, [, \, ] with respectively `, {, |, } and ^, among other pairs that you indiscriminately consider equivalent.
The index variables i and j should have type size_t to allow for arbitrary long strings.
The inner loop only tests for *(p + j) == '\0' if the characters match, hence the function only matches the needle at the end of the haystack string.
Using the pointer syntax *(p + j) == '\0' is cumbersome and less readable than the equivalent array syntax p[j] == '\0'.

Here is a modified version using the standard header <ctype.h>:

#include <ctype.h>

char *strstrci(const char *s, const char *p) {
    if (*p == '\0')
        return (char *)s;
    for (; *s; s++) {
        if (tolower((unsigned char)*s) == tolower((unsigned char)*p)) {
            size_t i;
            for (i = 1;; i++) {
                if (p[i] == '\0')
                    return (char *)s;
                if (tolower((unsigned char)s[i]) != tolower((unsigned char)p[i]))
                    break;
            }
        }
    }
    return NULL;
}