(49G & 38G & Prime) OEIS A111138: No Short Description

[Gerald H]

For natural number input N the programme below returns the Nth element of the series

https://oeis.org/A111138

described as

"For a subgroup H of order p^n (p an odd prime) of the subgroup generated by all commutators [x_j,x_i] in the relatively free group F of class three and exponent p, freely generated by x_1, x_2,..., x_k, (k sufficiently large) the minimum size of the subgroup of [H,F] of F_3 is p^{kn - a(n)}.
The sequence arises when finding a purely numerical sufficient condition for the capability of p-groups of class two and exponent p, where p is an odd prime."

Whatever you make of the description, the programme below is fairly simple but slow.

Could everyone please try to find a faster programme &/or a better algorithm?

The sub-programme ID ISQRT is here

http://www.hpmuseum.org/forum/thread-383...quare+root

Size: 179.5

CkSum: # 36635d

Code:

::
  CK1&Dispatch
  # FF
  ::
    ZINT 0
    SWAP
    BEGIN
    DUP
    ZINT 3
    Z>
    WHILE
    ::
      ZINT 1
      FPTR2 ^RSUBext
      DUP
      ZINT 8
      FPTR2 ^RMULText
      ZINT 1
      FPTR2 ^RADDext
      ID ISQRT
      DROP
      ZINT 1
      FPTR2 ^RSUBext
      DUP
      FPTR2 ^ZAbs
      FPTR2 ^QIsZero?
      ?SEMI
      ZINT 2
      FPTR2 ^ZQUOText
      FPTR2 ^RSUBext
      DUPUNROT
      FPTR2 ^RADDext
      SWAP
    ;
    REPEAT
    ZINT 3
    EQUAL
    NOT?SEMI
    ZINT 1
    FPTR2 ^RADDext
  ;
;