We define n♡ recursively as follows.
1♡=1; n♡=((n−1)♡)⋅n+1
Find the largest n<1000 such that the last two digits of n♡ are zeroes.
Just to make it clear: unlike "n-factorial," "n-heart" is NOT an official mathematical terminology.
919♡ = 19328918...75566100
but I haven't yet come up with a number-theoretic argument.
The values of n where n♡ ends in 00 are
19 107 119 207 219 307 319 407 419 507 519 607 619 707 719 807 819 907 919
It appears that there's a pattern there, no? More thought needed.