[seqfan] n % sopfr(n)

[jnthn stdhr]

Seqfans,

I found that the sequence produced by n % sopfr(n) is not in the database,
so I am proposing this as A238525, along with a few related sequences.
A238528 lists record prime values of A238525, which appears to be identical
to A001359 ("Lesser of twin primes"), except a(1) = 2, and a(4) = 7 are
inserted.

  A238529 (tentatively named "Recursive depth of n % sopfr(n).") is a
recursive version of A238525 and counts the number of times the operation
can be applied to n.  For example, with n=166, 166 % sopfr(166) = 166 % 85
= 81;  81 % sopfr(81) = 81 % 12 = 9;  9 % sopfr(9)  = 9 % 6 = 3; finally, 3
% sopfr(3) = 3 % 3 = 0, so the depth of 166 is 4.  A238530 lists the least
number with depth n, and currently has just eight terms (2, 8, 22, 166,
778, 4962, 29922, 179682).

  Any help extending A238525-A238530, A238530 in particular, would be much
appreciated.

Jonathan