+- HP Forums (https://www.hpmuseum.org/forum)
+-- Forum: HP Software Libraries (/forum-10.html)
+--- Forum: General Software Library (/forum-13.html)
+--- Thread: (49G & 38G & Prime) OEIS A111138: No Short Description (/thread-9514.html)
(49G & 38G & Prime) OEIS A111138: No Short Description - Gerald H - 11-17-2017 09:35 AM
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-3837.html?highlight=square+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
;
;RE: (49G) OEIS A111138: No Short Description - Arno K - 11-18-2017 02:04 PM
I made an algorithm by myself, my apologies if it is similar to yours (I hope not as you don't seem to use a root), my capabilities in reading sysrpl are limited, the program is for the prime and a MAKELIST(A111138(x),x,1,64) provides exactly the same list as in OEIS, it is quite fast and the algorithm is visible (one of the reasons for which I put my 50g into a drawer).
Code:
#cas
A111138(n):=
BEGIN
local m,s;
IF n<3 THEN RETURN 0;END;
IF n≤4 THEN RETURN 1;END;
m:=FLOOR(0.5+0.5*√(8*n+1));
WHILE m*(m-1)≥2*n DO
m:=m-1;
END;
s:=n-m*(m-1)/2;
return COMB(m,3)+COMB(s,2);
END;
#endRE: (49G) OEIS A111138: No Short Description - Gerald H - 11-18-2017 02:52 PM
Congratulations, Arno K, a very nice programme for which you should certainly not apologize.
Here a programme for the 38G.
The complications with the IFTE structures are due to the COMB function in the 38G returning an error for
COMB(a,b)
if a<b, whereas the Prime returns 0.
A111138P
Code:
Ans►N:
IF
Ans==1
THEN
0:
ELSE
ROUND(√(2*Ans),0)►R:
N-COMB(Ans,2):
IFTE(Ans>1,COMB(Ans,2),0)+IFTE(R>2,COMB(R,3),0):
END:RE: (49G) OEIS A111138: No Short Description - Gerald H - 11-18-2017 03:40 PM
On the 49G the 38G programme works nicely as:
Code:
« DUPDUP 2. * √ 0.
RND R→I DUP 3 COMB
UNROT 2 COMB - 2
COMB + SWAP DROP
»Fortunately, from the 49G on, for
a<b
COMB(a,b)
returns
0
rather than an error. 42S & 48G return error.
RE: (49G) OEIS A111138: No Short Description - Gerald H - 11-18-2017 04:13 PM
Here a SysRPL version of the programme above.
ID SQRT0
finds the closest integer square root & is available here
http://www.hpmuseum.org/forum/thread-8992.html?highlight=square+root
PTR 2EF19
is internal COMB, same address since 1.19-6.
Size: 77.
CkSum: # 6728h
Code:
::
CK1&Dispatch
# FF
::
DUPDUP
FPTR2 ^RADDext
ID SQRT0
DUP
ZINT 3
PTR 2EF19
3UNROLL
ZINT 2
PTR 2EF19
FPTR2 ^RSUBext
ZINT 2
PTR 2EF19
FPTR2 ^RADDext
;
;RE: (49G) OEIS A111138: No Short Description - Gerald H - 11-18-2017 04:28 PM
And here a programme to insert symbolics in the Sequence App of the 38G to produce the series:
Code:
RECURSE(U,IFTE(U3(N)>1,COMB(U3(N),2),0)+IFTE(U2(N)>2,COMB(U2(N),3),0),0,0)►U1(N):
CHECK 1:
RECURSE(U,ROUND(√(2*N),0),1,2)►U2(N):
RECURSE(U,N-COMB(U2(N),2),0,0)►U3(N):
RECURSE(U,U3(N)-1,0,0)►U4(N):
CHECK 4:RE: (49G & 38G & Prime) OEIS A111138: No Short Description - Arno K - 11-18-2017 04:33 PM
I hope your new program runs faster than the old one.
Arno
RE: (49G & 38G & Prime) OEIS A111138: No Short Description - Gerald H - 11-18-2017 04:48 PM
Yes, it certainly does, & I believe faster than yours, if you could translate it to run on Prime.
RE: (49G & 38G & Prime) OEIS A111138: No Short Description - Arno K - 11-18-2017 05:38 PM
Quite clear, you leave out the loop to determine the best m, perhaps that will be necessary if n increases, I don't know as I haven't checked that.
Arno
Edit: I now verified that I can leave out that loop, as it never will be executed, but I will leave the source above as it is.
RE: (49G & 38G & Prime) OEIS A111138: No Short Description - Gerald H - 11-18-2017 06:04 PM
It might be a good idea to publish your finished programme in the Prime Software Library.
RE: (49G & 38G & Prime) OEIS A111138: No Short Description - Arno K - 11-18-2017 06:27 PM
Have you checked n=7? I get 7 on my Prime instead of 4.
RE: (49G & 38G & Prime) OEIS A111138: No Short Description - Gerald H - 11-18-2017 07:14 PM
Input
7
returns
4
on all my programmes.
RE: (49G & 38G & Prime) OEIS A111138: No Short Description - Arno K - 11-18-2017 08:00 PM
Got it: 0. RND rounds nearest, FLOOR clearly down.
Arno
RE: (49G & 38G & Prime) OEIS A111138: No Short Description - Gerald H - 11-19-2017 08:25 AM
Another programme for the 38G using the COMB0 programme available here
http://www.hpmuseum.org/forum/thread-9530.html
Code:
Ans►N:
ROUND(√(2*Ans),0)►R:
(Ans,2):
RUN COMB0:
(N-Ans,2):
RUN COMB0:
Ans►T:
(R,3):
RUN COMB0:
Ans+T:RE: (49G & 38G & Prime) OEIS A111138: No Short Description - John Keith - 07-05-2019 01:57 PM
My apologies for bringing up an old thread, but I was looking at the OEIS page and i was struck by the last comment: "Partial sums of A002262." This inspired the following program which returns a list of the first T(n) terms, where T(n) is the nth triangular number.
It is reasonably fast: an input of 45 returns the first 1035 terms in about 4.14 seconds on my HP 50. The program requires the ListExt and GoferLists libraries. It could be rewritten without them but the program would be longer and slower.
Code:
\<< \-> n
\<< 0 n 1 -
FOR k 0 k LSEQR
NEXT n \->LIST LXIL
\<< +
\>> Scanl1
\>>
\>>